1. Participants must have locally advanced or unresectable histologically or cytologically confirmed WD G3 NET. * pancreas primary. * other primary sites: gastrointestinal site, unknown primary site, lung neuroendocrine carcinoma with carcinoid morphology, or other non-pancreatic primary sites with well-differentiated (WD) morphology and Ki67 \> 20%. * WD G3 NET occurring de novo or in the setting of grade progression allowed (provided WD G3 NET is thought to be the dominant histology at the time of enrollment). * Tumors with ambiguous histology and/or Ki67 \>/=55% must be reviewed at the participating site to confirm that they are not poorly differentiated. Tumors with confirmed ambiguous histology will be considered eligible. 2. At least 1 measurable target lesion according to RECIST 1.1, including the following criteria. * non-nodal lesion that measures \>=1.0 cm in the longest diameter. * lymph node (LN) lesion that measures as \>=1.5 cm in the short axis. * the lesion is suitable for repeat measurement using computed tomography (CT) / magnetic resonance imaging (MRI) (CT/MRI). * the lesion is not \<1.5 cm and the only measurable site available for pre-treatment biopsy. * lesions previously treated with radiation or other locoregional therapy are considered measurable if progression has been demonstrated in such lesions. * in the setting of grade progression, every attempt should be made to select measurable target lesions that are thought to represent G3 disease (based on biopsy results, tumor growth rate, or other features). 3. University of California, San Francisco (UCSF) participants only-eligibility for Hyperpolarized 13C (C13 HP) MRI * At least two measurable lesions that are \>=1.0 cm in diameter, at least one accessible to percutaneous core needle biopsy, and one (ideally separate from biopsy site) amenable to metabolic MRI. * No contraindications to MRI. * No prior local therapy to the target lesions (s) -unless clear progression in the lesions(s). 4. Radiographic evidence of progressive disease within 6 months (Required unless \>50% liver involvement and/or Ki67 \> 30%). 5. Progression on at least one prior line of therapy if Ki67 \< 30%. 6. Age \>=18 years (No dosing or adverse event data are currently available on the use of lenvatinib plus pembrolizumab in patients \<18 years of age, children are excluded from this study but will be eligible for future pediatric trials). 7. Eastern Cooperative Oncology Group (ECOG) performance status \<= 1. 8. Have adequate organ function as defined below (Specimens must be collected within 14 days prior to the start of study treatment): * Adequate bone marrow function: * Absolute neutrophil count \>=1,500/microliter (mcL) * Platelets \>=100,000/mcL * Hemoglobin \>=1,500/mcL * Hemoglobin \>=9.0 g/dL or \>=5.6 mmol/L. * Adequate hepatic function, * Total bilirubin \<=1.5 X institutional upper limit of normal, unless elevated due to Gilbert's syndrome and direct bilirubin is within normal limits. * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT) (serum glutamic-pyruvic transaminase (SGPT) \<=2.5 X institutional upper limit of normal (ULN) (\<=5 × ULN for participants with liver metastases). * Adequate renal function, * Creatinine \<= 1.5 x institutional upper limit of normal OR * Creatinine clearance \>=30 mL/min for participant with creatinine levels \>1.5 × institutional ULN, * Urine protein-to-creatinine ratio (UPCR) \<1 (unless urine protein \<1 g/24 hour) OR * Urine protein dipstick \<= 1+(unless urine protein \<1 g/24 hour). * Coagulation: International normalized ratio (INR) OR prothrombin time (PT) Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) \<=1.5 × ULN unless participant is receiving anticoagulant therapy (and PT or aPTT is within therapeutic range of intended use of anticoagulants). 9. Participant (or legally acceptable representative) must have the ability to understand a written informed consent document, and the willingness to sign it. 10. Adequately controlled blood pressure (BP) with or without anti-hypertensive medications, defined as BP \<140/90 (NOTE: BP should be controlled without a change in medications within one week of day 1 cycle 1). 11. Individuals with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. 12. Must have a life expectancy of greater than 3 months, as determined by the investigator. 13. Stage 1 (if undergoing C13 HP MRI) and Stage 2: Patients must agree to have a biopsy of the primary tumor or metastatic tissue at baseline, and there must be a lesion that can be biopsied with acceptable clinical risk (as judged by the investigator). * Patients with unsuccessful baseline biopsies may undergo an additional biopsy attempt (at the same or a different site, determined by the investigator). * For patients with an intact primary and no metastatic site that can be safely biopsied, a biopsy of the primary is acceptable, but must be approved by the principal investigator. * Baseline tumor biopsy may be omitted if the tumor is inaccessible and/or a biopsy is thought to post high procedural risk due to location or other factors: ••If participants have only 1 measurable lesion per RECIST 1.1, the biopsy specimen should be obtained from a non-target lesion (or archival tissue should be used). * If fresh tumor tissue cannot be collected, the overall study (lead-site) principal investigator may approve the use of archival tissue. The use of archival tissue in lieu of a fresh tumor biopsy will be evaluated on a case-by-case basis and must be approved by the overall study (lead-site) PI. ••Formalin-fixed, paraffin-embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue. * Stage 1 patients who are not undergoing C13 HP MRI can omit baseline biopsy. ••Use of archived tissue is encouraged if accessible. 14. Male participants are eligible to participate if they agree to the following starting with the first dose of study therapy through 7 days after the last dose of lenvatinib (and refrain from donating sperm during this period). (Note that 30 days after lenvatinib is stopped, if the participant is on pembrolizumab only, no male contraception measures are needed.) * Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) and agree to remain abstinent OR Must agree to use contraception (see appendix 5) unless confirmed to be azoospermic (vasectomized or secondary to medical cause) as detailed below: * Agree to use a male condom plus partner use of an additional contraceptive method when having penile-vaginal intercourse with a WOCBP who is not currently pregnant. Note: Men with a pregnant or breastfeeding partner must agree to remain abstinent from penile-vaginal intercourse or use a male condom during each episode of penile-vaginal penetration. * Please note that 7 days after lenvatinib is stopped, if the participant is on pembrolizumab only, no male contraception measures are needed. 15. Female participants are eligible if not pregnant or breastfeeding, and at least 1 of the following conditions applies during the intervention period and for at least 120 days post pembrolizumab or 30 days post lenvatinib, whichever occurs last: * Not be a woman of childbearing potential (WOCBP), e.g., postmenopausal (no menses for \> 1 year) or permanently sterilized. * Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), with low user dependency. * Abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) NOTE: The investigator should evaluate the potential for contraceptive method failure (i.e., noncompliance, recently initiated) in relationship to the first dose of study intervention.