Capecitabine and Lenvatinib With External Radiation in Rectal Adenocarcinoma

Inclusion Criteria: * Histologically (archival tissue) confirmed adenocarcinoma of the rectum that begins within 12 cm of the anal verge as determined by sigmoidoscopy and/or colonoscopy with no evidence of distant metastasis. * Locally advanced rectal cancer determined by any of the following features: 1.) Fixed or immobile tumor on physical exam and/or; 2.) T3 disease with invasion through the muscularis propria as defined by transrectal ultrasound, CT or MRI; 3.) T4 disease with invasion of adjacent structures such as pelvic sidewall, sacrum, pelvis, bladder and/or prostate as determined appropriate imaging modalities such as ultrasound, CT or MRI; 4.) Any T with + N on CT scan/MRI or transrectal ultrasound. * Age equal to or greater than 18 years * Eastern Cooperative Oncology Group (ECOG) Performance Status 0 or 1. * Adequate bone marrow, liver and renal function. * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment. * Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation. Men should use adequate birth control for at least 3 months after the last administration of lenvatinib. * Ability to understand and the willingness to sign a written informed consent. A signed informed consent must be obtained prior to any study specific procedures. Exclusion Criteria: * Cardiac disease: Congestive heart failure \> class II New York Heart Association (NYHA). Participants must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months. * Previous pelvic irradiation therapy. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * Uncontrolled hypertension defined as systolic blood pressure \> 150 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management. * Known human immunodeficiency virus (HIV) infection or chronic hepatitis B or C. * Active clinically serious infection \> CTCAE Grade 2. * Thrombotic or embolic events such as a cerebrovascular accident including transient ischemic, attacks, deep vein thrombosis (DVT) within the past 6 months. * Bleeding or thrombotic disorders or use of anticoagulants, such as warfarin, or similar agents requiring therapeutic international normalized ration (INR) monitoring. (Treatment with low molecular weight heparin (LMWH) is allowed). * Active malignancy except for non-melanoma skin cancer or in situ cervical cancer or treated non-pelvic cancer from which the patient has been continuously disease free more than 3 years. * Marked baseline prolongation of QT/QTc interval (QTc interval ≥ 500 msec) using the Fridericia method (QTc = QT/RR0.33) for QTc analysis. * Greater than 30 mg/dL on urine analysis. Patients with \>30 mg/dL on urine analysis on urine analysis will undergo 24-hour urine collection for quantitative assessment of proteinuria. Patients with 24-hour protein ≥1 g/24 hours will be ineligible. * Needing medical attention for serious bleeding in past 4 weeks. * Previous chemotherapy except for antiangiogenic agent or tyrosine kinase inhibitor (TKI) will be allowed as long as it is more than 5 years. * Major surgeries within 3 weeks of starting chemotherapy. * Evidence or history of bleeding diathesis. * Use of St. John's Wort or rifampin. * Known or suspected allergy to lenvatinib or any agent given in the course of this trial. * Any condition that impairs participant's ability to swallow whole pills. * Any malabsorption problem. * Medical need for the continued use of potent inhibitors/inducers of CYP3A4. * Creatinine clearance not within study guidelines.