Lenvatinib and Pembrolizumab Maintenance Therapy for the Treatment of Patients of Advanced Unresectable Pancreatic Cancer

Inclusion Criteria:

* Documented informed consent by the participant
* Willingness to provide tissue and blood samples for correlative studies
* Age: \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 1
* Must have a confirmed histologic or cytologic diagnosis of advanced unresectable pancreatic ductal adenocarcinoma (PDA)
* Must have received at least 16 weeks of 1st or 2nd line therapy and achieved partial response or stable disease (by computed tomography \[CT\] or magnetic resonance imaging \[MRI\]) with no signs of progression within 30 days before start of treatment
* Last chemotherapy treatment must be within 30 days prior to start of treatment
* No prior therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137)
* Measurable or evaluable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions
* Participants must have recovered from all adverse events (AEs) due to previous therapies to =\< grade 1 or baseline, with the following exception: participants with =\< grade 2 neuropathy are eligible

  * Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent
* A male participant must agree to use a contraception of this protocol during the treatment period and for at least 90 days after the last dose of study treatment and refrain from donating sperm during this period
* A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies:

  * Not a woman of childbearing potential (WOCBP) OR
  * Females of child-bearing potential must be willing to use effective contraception during study and for 30 days after the last dose
* Hemoglobin \>= 9.0 g/dL or \>= 5.6 mmol/L. Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks (performed within 14 days prior to day 1)
* Absolute neutrophil count (ANC) \>= 1,500/mm\^3 (performed within 14 days prior to day 1)
* Platelets \>= 100,000/mm\^3 (performed within 14 days prior to day 1)
* Total serum bilirubin =\< 1.5 x upper limit of normal (ULN) OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 x ULN (performed within 14 days prior to day 1)
* Aspartate Aminotransferase =\< 1.5 x ULN or =\< 3 x ULN with liver metastases (performed within 14 days prior to day 1)
* Alanine aminotransferase (ALT) =\< 1.5 x ULN or =\< 3 x ULN with liver metastases (performed within 14 days prior to day 1)
* Creatinine =\< 1.5 x ULN OR calculated creatinine clearance \>= 30 mL/min for participant with creatinine levels \>1.5 x institutional ULN (performed within 14 days prior to day 1)
* International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulants (performed within 14 days prior to day 1)
* aPTT =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants (performed within 14 days prior to day 1)
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test

  * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required

Exclusion Criteria:

* Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug
* Dietary/herbal supplements (cannabidiol \[CBD\] allowed)
* Other investigational products
* Current or planned se of agents contraindicated for use with strong CYP3A4 inducers
* Strong inhibitors or inducers of CYP3A
* Medications with a known potential to prolong the QT/corrected QT (QTc) interval
* Issues with tolerating oral medication (e.g. inability to swallow pills, malabsorption issues, ongoing nausea or vomiting during screening)
* Uncontrolled blood pressure (systolic blood pressure \[BP\] \> 140 mmHg or diastolic BP \> 90 mmHg) in spite of an optimized regimen of antihypertensive medication
* Women who are or are planning to become pregnant or breastfeed
* Known allergy to any of the components within the study agents and/or their excipients
* 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 at least two years
* Participants must not have received radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (=\< 2 weeks of radiotherapy) to non-central nervous system (CNS) disease
* Participants must not have known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study intervention

  * Participants may not be currently participating in or participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study intervention
* Intercurrent or historic medical condition that increases subject risk in the opinion of the Investigator. Eligibility may be revisited for intercurrent medical conditions once resolution/recovery is deemed adequate by the investigator (e.g. recovery from major surgery, completion of treatment for severe infection)
* Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist) are live attenuated vaccines and are not allowed
* Has active autoimmune disease that has required systemic treatment in the past 2 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, etc.) is not considered a form of systemic treatment and is allowed
* Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis
* Has an active infection requiring systemic therapy
* Has a known history of human immunodeficiency virus (HIV) infection
* Has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (defined as hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) infection. Note: no testing for Hepatitis B and hepatitis C is required unless mandated by local health authority
* Has a known history of active TB (Mycobacterium tuberculosis)
* Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
* Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment
* Has had an allogenic tissue/solid organ transplant
* Electrolyte abnormalities that have not been corrected
* Significant cardiovascular impairment: history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or stroke within 6 months of the first dose of study drug, or cardiac arrhythmia requiring medical treatment at Screening
* Bleeding or thrombotic disorders or subjects at risk for severe hemorrhage

  * The degree of tumor invasion/infiltration of major blood vessels (e.g. carotid artery) should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy
* Subjects having \> 1+ proteinuria on urine dipstick testing unless a 24-hour urine collection for quantitative assessment indicates that the urine protein is \< 1 g/24 hours
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)