Lenvatinib and Everolimus in Treating Patients With Advanced, Unresectable Carcinoid Tumors

Inclusion Criteria: * Histologically or cytologically confirmed unresectable well differentiated (irrespective of grade) carcinoid tumors. Patients with multiple neuroendocrine tumors associated with MEN1 syndrome will be eligible * Patients must have radiographically measurable disease. Lesions that have had locoregional therapies such as radiofrequency (RF) ablation, radiation or transarterial therapies must show evidence of progressive disease based on RECIST 1.1 to be deemed a target lesion. * Patients with other gastrointestinal neuroendocrine tumors must have had progressive disease over the last 12 months irrespective of number of prior therapies. Patients with both functional (who may continue somatostatin analogues as required for control of related symptoms) and non-functional tumors are eligible. * Written informed consent must be obtained prior to any screening procedures. * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 - 1. * A sufficient interval must have elapsed between the last dose of prior anti-cancer therapy (including cytotoxic and biological therapies and major surgery) and enrollment, to allow the effects of prior therapy to have abated: * Cytotoxic or targeted chemotherapy: \>= the duration of the cycle of the most recent treatment regimen (a minimum of 3 weeks for all regimens, except 6 weeks for nitrosoureas and mitomycin-C) * Biologic therapy (e.g., antibodies): \>= 4 weeks. * Absolute neutrophil count…