Pembrolizumab Every 12 Weeks Versus Every 3 Weeks in Treating Patients With Non-small Cell Lung Cancer

Inclusion Criteria:

* Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 at the time of study treatment initiation.
* Have pathologically confirmed diagnosis of non-small cell lung cancer (NSCLC). Mixed small cell lung cancer (SCLC) histology is not allowed.
* Must be eligible for treatment with pembrolizumab as standard of care (up to third line).
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L.
* Platelets \>= 100 x 10\^9/L.
* Hemoglobin \>= 9 g/dL.
* Plasma creatinine =\< 1.5 x institution upper limit of normal (ULN) or estimated glomerular filtration rate (GFR) (measured or calculated with Cockcroft and Gault formula) \> 45 ml/min.
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN (ALT and AST =\< 5 x ULN is acceptable if liver metastases are present).
* Total plasma bilirubin =\< 1.5 x ULN. For patients with well documented Gilbert?s syndrome, total bilirubin =\< 3 x ULN with direct bilirubin within normal range.
* Must have demonstrated complete response, partial response by Response Evaluation Criteria in Solid Tumors (RECIST) or stable disease if \> 5% but less than 30% decrease from baseline total tumor burden (target lesions) to pembrolizumab at the time of randomization for study treatment.Patients with new brain metastasis isolated in the brain while on pembrolizumab monotherapy will be eligible as long as extracranial disease control fulfills the criteria otherwise (i.e. this will not be considered as disease progression for the purpose of this study).
* Must have received at least 6 months of pembrolizumab monotherapy treatment (but no more than 15 months total duration, including treatment in combination with chemotherapy prior to maintenance phase) prior to start of protocol-assigned treatment.
* Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.
* Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure.

Exclusion Criteria:

* Receipt of anticancer chemotherapy, other than pembrolizumab, within 6 months prior to randomization.
* Disease progression to pembrolizumab as assessed by immune related (ir)RECIST.
* Prior radiotherapy or gamma knife within 2 weeks of study treatment for non-brain metastasis. Subjects must have recovered from all radiation related toxicities.
* Active/untreated brain metastasis. Whole brain radiation or gamma knife radiosurgery performed less than 4 weeks prior to first administration of study drug. Previously treated brain metastasis allowed as long as not requiring steroids and stable on imaging at least 4 weeks after completing radiation therapy.
* Leptomeningeal involvement regardless of tumor response status.
* Tumor with mutation that is known to be sensitive to Food and Drug Administration (FDA)- approved targeted therapy.
* Patients who had pembrolizumab interrupted for more than 4 weeks for management of treatment-related adverse event.
* Currently receiving or has received high-dose systemic corticosteroids within 4 weeks prior to starting study drug for management of brain metastases, or who have not fully recovered from side effects of such treatment. Patients who are on low-dose prednisone (10 mg once daily or less) for at least 6 months for the management of other chronic disorders (e.g. chronic obstructive pulmonary disease \[COPD\]) is allowed. Steroids for endocrine replacement or receipt of short-course of steroids during the preceding 4 week period as supportive medication such as for drug allergy, anti-emetic, etc. is allowed.
* Had major surgery within 14 days prior to starting protocol treatment.
* Active, clinically serious infections or other serious uncontrolled medical conditions.
* Pregnant or nursing female participants.
* Any condition which in the investigator?s opinion deems the participant an unsuitable candidate to receive study drug.
* Unwilling or unable to follow protocol requirements.