Ramucirumab and Pembrolizumab Versus Standard of Care in Treating Patients With Stage IV or Recurrent Non-small Cell Lung Cancer (A Lung-MAP Non-Match Treatment Trial)

Inclusion Criteria:

* Patients must have been assigned to S1800A by the Southwest Oncology Group (SWOG) Statistics and Data Management Center (SDMC). Patients who were screened under S1400 (legacy screening/pre-screening study) must have had prior PD-L1 testing by the Dako 22C3 PharmDx immunohistochemistry (IHC) assay, and must have results available for stratification purposes
* Patients must not have EGFR sensitizing mutations, EGFR T790M mutation, ALK gene fusion, ROS 1 gene rearrangement, and BRAF V600E mutation unless they have progressed following all standard of care targeted therapy
* Patients must not have an active autoimmune disease that has required systemic treatment in past two years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed
* Patients must not have any history of primary immunodeficiency
* Patients must not have experienced the following:

  * Any grade 3 or worse immune-related adverse event (irAE). Exception: asymptomatic nonbullous/nonexfoliative rash
  * Any unresolved grade 2 irAE
  * Any toxicity that led to permanent discontinuation of prior anti-PD-1/PD-L1 immunotherapy

    * Exception to the above: Toxicities of any grade that requires replacement therapy and has stabilized on therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) are allowed
* Patients must not have any history of organ transplant that requires use of immunosuppressives
* Patients must not have clinical signs or symptoms of active tuberculosis infection
* Patients must not have history of (non-infectious) pneumonitis that required steroids or current pneumonitis/interstitial lung disease
* Patients must not have had a serious or nonhealing wound, ulcer, or bone fracture within 28 days prior to sub-study randomization
* Patients must not have a history of gastrointestinal perforation or fistula within six months prior to sub-study randomization
* Patients must not have grade 3-4 gastrointestinal bleeding (defined by National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 5) within three months prior to sub-study randomization
* Patients must not have any known allergy or reaction to any component of the investigational and standard of care formulations
* Patients must not have any grade III/IV cardiac disease as defined by the New York Heart Association criteria (i.e., patients with cardiac disease resulting in marked limitation of physical activity or resulting in inability to carry on any physical activity without discomfort), unstable angina pectoris, and myocardial infarction within six months prior to sub-study randomization, or serious uncontrolled cardiac arrhythmia
* Patients must not have experienced any arterial thromboembolic events, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, within six months prior to sub-study randomization
* Patients must not have documented evidence of acute hepatitis or have an active or uncontrolled infection
* Patients with known human immunodeficiency virus (HIV) infection are eligible, provided they are on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test and within 6 months prior to randomization
* Patients with evidence of chronic hepatitis B virus (HBV) infection are eligible provided viral load is undetectable on suppressive therapy, if indicated
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Patients must not have undergone major surgery within 28 days prior to sub-study randomization, or subcutaneous venous access device placement within 7 days prior to randomization. Any patient with postoperative bleeding complications or wound complications from a surgical procedure performed in the last two months should be excluded. The patient must not have elective or planned major surgery to be performed during the course of the clinical trial
* Patients must not have gross hemoptysis within two months of sub-study randomization (defined as bright red blood or \>= 1/2 teaspoon) or with radiographic evidence of intratumor cavitation or has radiologically documented evidence of major blood vessel invasion or encasement by cancer
* No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for five years
* Patients must not have been diagnosed with venous thrombosis less than 3 months prior to randomization. Patients with venous thrombosis diagnosed more than 3 months prior to randomization must be on stable doses of anticoagulants
* Patients must not have any of following:

  * Cirrhosis at a level of Child-Pugh B (or worse);
  * Cirrhosis (any degree) and a history of hepatic encephalopathy; or
  * Clinically meaningful ascites resulting from cirrhosis. Clinically meaningful ascites is defined as ascites from cirrhosis requiring diuretics or paracentesis
* Patients must have received exactly one line of anti-PD-1 or anti-PD-L1 therapy for at least 84 days as their most recent line of therapy, either alone or in combination with platinum-based chemotherapy. Patients must have experienced disease progression during or after this regimen. Patients whose most recent line of therapy was anti-PD-1 or anti-PD-L1 monotherapy must have also experienced disease progression during or after prior platinum-based chemotherapy
* Patients must not have received any prior systemic therapy (systemic chemotherapy, immunotherapy or investigational drug) within 21 days prior to substudy randomization. Patients must have recovered (=\< grade 1) from any side effects of prior therapy, except for alopecia. Patients must not have received any radiation therapy within 14 days prior to sub-study randomization
* Patients must not have received nitrosoureas or mitomycin-c within 42 days prior to sub-study randomization
* Patients must not have received systemic treatment with corticosteroids (\> 10 mg daily prednisone or equivalent) or other immunosuppressive medications within seven days prior to sub-study randomization. Inhaled or topical steroids, and adrenal replacement doses =\< 10 mg daily prednisone or equivalent are permitted in the absence of active autoimmune disease
* Patients must not have received a live attenuated vaccination within 28 days prior to sub-study randomization
* Patients must not be planning to receive any concurrent chemotherapy, immunotherapy, biologic or hormonal therapy for cancer treatment while receiving treatment on this study. Concurrent use of hormones for non-cancer-related conditions (e.g., insulin for diabetes and hormone replacement therapy) is acceptable
* Patients must not be receiving chronic antiplatelet therapy, including aspirin, nonsteroidal anti-inflammatory drugs (NSAIDs, including ibuprofen, naproxen, and others), dipyridamole or clopidogrel, or similar agents within 7 days prior to randomization. Once-daily aspirin use (maximum dose 325 mg/day) is permitted
* Patient must not have received radiotherapy within 14 days before the first dose of study treatment or received lung radiation therapy of \> 30 Gy within 6 months before the first dose of study treatment

  * Note: Participants must have recovered from all radiation-related toxicities to grade 1 or less, not require corticosteroids, and not have had radiation pneumonitis
* Patients must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI). The CT from a combined positron emission tomography (PET)/CT may be used to document only non-measurable disease unless it is of diagnostic quality. Measurable disease must be assessed within 28 days prior to substudy randomization. Pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease. Non-measurable disease must be assessed within 42 days prior to sub-study randomization. All disease must be assessed and documented on the Baseline Tumor Assessment Form. Patients whose only measurable disease is within a previous radiation therapy port must demonstrate clearly progressive disease (in the opinion of the treating investigator) prior to sub-study randomization. CT and MRI scans must be submitted for central review via transfer of images and data (TRIAD)
* Patients must have a CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 days prior to sub-study randomization. Patient must not have leptomeningeal disease, spinal cord compression or brain metastases unless: (1) metastases have been locally treated and have remained clinically controlled and asymptomatic for at least 14 days following treatment, and prior to sub-study randomization, AND (2) patient has no residual neurological dysfunction and has been off corticosteroids for at least seven days prior to sub-study randomization
* Absolute neutrophil count (ANC) \>= 1,500/mcl (obtained within 28 days prior to sub-study randomization)
* Platelet count \>= 100,000 mcl (obtained within 28 days prior to sub-study randomization)
* Hemoglobin \>= 9 g/dL (obtained within 28 days prior to sub-study randomization)
* Serum bilirubin =\< institutional upper limit of normal (IULN) within 28 days prior to sub-study randomization. For patients with liver metastases, bilirubin must be =\< 5 x IULN; and either
* Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) =\< 2 x IULN within 28 days prior to sub-study randomization (if both ALT and AST are done, both must be \< 2 IULN). For patients with liver metastases, either ALT or AST must be =\< 5 x IULN (if both ALT and AST are done, both must be =\< 5 x IULN)
* Serum creatinine =\< the IULN OR calculated creatinine clearance \>= 50 mL/min using the Cockcroft-Gault formula. This specimen must have been drawn and processed within 28 days prior to sub-study randomization
* Patients? urinary protein must be =\< 1+ on dipstick or routine urinalysis (UA). If urine dipstick or routine analysis indicated proteinuria \>= 2+, then a 24-hour urine is to be collected and demonstrate \< 1000 mg of protein in 24 hours to allow participation in the study
* Patients must not have a history of uncontrolled or poorly-controlled hypertension (defined as \>= 150 / \>= 90 mm Hg for \> 4 weeks) despite standard medical management
* International normalized ratio (INR) =\< 1.5 (documented within 28 calendar days prior to randomization)
* Partial thromboplastin time (PTT) =\< 5 seconds above the institutional upper limit of normal (IULN) (unless receiving anticoagulation therapy) (documented within 28 calendar days prior to randomization)
* Patients receiving warfarin must be switched to low molecular weight heparin and have achieved stable coagulation profile 14 days prior to randomization. If receiving warfarin, the patient must have an INR =\< 3.0. For heparin and low molecular weight heparin (LMWH) there should be no active bleeding (that is, no bleeding within 14 days prior to first dose of protocol therapy) or pathological condition present that carries a high risk of bleeding (for example, tumor involving major vessels or known varices)
* Patients must have Zubrod performance status 0-1 documented within 28 days prior to sub-study randomization
* Pre-study history and physical exam must be obtained within 28 days prior to substudy randomization
* Patients must not be pregnant or nursing. Women/men of reproductive potential must have agreed to use an effective contraceptive method during the study and 4 months after study completion. A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures during the study and 4 months after study completion
* Patients must agree to have blood specimens submitted for circulating tumor DNA (ctDNA)
* Patients must also be offered participation in banking and in the correlative studies for collection and future use of specimens
* As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system
* Patients with impaired decision-making capacity are eligible as long as their neurological or psychological condition does not preclude their safe participation in the study (e.g., tracking pill consumption and reporting adverse events to the investigator)
* Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines