Inclusion Criteria:  Histologically or cytologically confirmed malignant secretory or non-secretory pheochromocytoma or paraganglioma that is unresectable and deemed inappropriate for alternative local regional therapeutic approaches Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 Life expectancy > 24 weeks Absolute neutrophil count (ANC) >= 1500/mm^3 White blood cell (WBC) count >= 3,000/mm^3 Platelet count >= 100,000/mm^3 Hemoglobin >= 9.0 g/dL (5.6 mmol/L); NOTE: transfusions are not allowed =< 7 days prior to registration Total bilirubin =< 1.5 X upper limit of normal (ULN) (or total bilirubin =< 3.0 X ULN with direct bilirubin =< 1.5 X ULN in patients with well-documented Gilbert's Syndrome) Aspartate transaminase (AST/serum glutamic oxaloacetic transaminase [SGOT]) =< 2.5 X ULN Creatinine =< 1.5 x ULN Urine protein/creatinine ratio =< 1 OR 24-hour urine protein < 1.5 gram Negative pregnancy test done =< 7 days prior to registration, for women of childbearing potential only Blood pressure (BP) < 150 mmHg (systolic) and < 90 mmHg (diastolic); initiation or adjustment of BP medication is permitted prior to registration provided that the average of three BP readings at a visit prior to registration is < 150/90 mmHg; NOTE: all patients with secretory pheochromocytoma or paraganglioma are REQUIRED to: 1) be evaluated in consultation by a hypertension specialist with specific experience in the management of hypertension in the setting of catecholamine-secreting tumors (usually an endocrinologist, nephrologist, or a cardiologist), and in the setting of hormone-associated hypertension) receive alpha- and beta-adrenergic blockade for at least 7-14 days prior to initiation of lenvatinib; the hypertension specialist of record for each patient should be committed to closely following the patient during the clinical study with evaluation by said specialist required at cycle 1 and 2 and thereafter on an as needed basis Provide written informed consent Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) Ability to complete questionnaire(s) by themselves or with assistance  Exclusion Criteria:  Any of the following Pregnant women Nursing women Men or women of childbearing potential who are unwilling to employ adequate contraception Chemotherapy/systemic therapy, radiotherapy, immunotherapy or surgery =< 21 days prior to registration or kinase inhibitor therapy =< 14 days prior to registration or failure to recover from toxicities (to grade 1 or below) from treatment; NOTE: concurrent therapy with octreotide is allowed providing that tumor progression on this therapy has been demonstrated; concurrent therapy with bisphosphonates (e.g. zoledronic acid) or denosumab is also allowed. Active or uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements Receiving any other investigational agent Current use of warfarin for any reason; NOTE: if patient can be safely transitioned to another anticoagulant, they may be eligible provided other criteria are satisfied Any of the following:  Correct QT (QTc) prolongation (defined as a QTc interval >= 500 msecs) Left ventricular ejection fraction (LVEF) < institutional lower limits of normal (LLN) Frequent ventricular ectopy Evidence of ongoing myocardial ischemia Receiving any medications or substances with risk of torsades de pointes; NOTE: medications or substances with known risk of torsades de pointes are prohibited; consult pharmacist for review if needed Known active and/or untreated brain metastases Known severe allergic or other prohibitive reactions to other tyrosine kinase inhibitors (TKI)  • Any of the following conditions: Active peptic ulcer disease Inflammatory bowel disease (e.g., ulcerative colitis, Crohn's disease) or other gastrointestinal conditions which increase the risk of perforation History of new abdominal fistula, gastrointestinal perforation or intra-abdominal abscess =< 84 days prior to registration; NOTE: enrollment of patients with chronic/canalized fistulous tracts (present for > 84 days) is allowed Serious or non-healing wound, ulcer, or bone fracture History of familial QTc prolongation syndrome  • Any of the following conditions =< 6 months prior to registration: Cerebrovascular accident (CVA) or transient ischemic attack (TIA) Serious or unstable cardiac arrhythmia Admission for unstable angina or myocardial infarction Cardiac angioplasty or stenting Coronary artery bypass graft surgery Pulmonary embolism, untreated deep venous thrombosis (DVT) or DVT which has been treated with therapeutic anticoagulation =< 30 days Arterial thrombosis Symptomatic peripheral vascular disease  • Other active malignancy =< 2 years prior to registration.