The overall purpose of this study is to determine the overall response rate, efficacy and safety of the combination of eribulin and Lenvatinib.

This is a phase II clinical trial of the combination of eribulin, and Lenvatinib. A cycle will be defined as 21 days. Eribulin will be given on days 1 and 8 of each cycle. Lenvatinib will be given daily during each cycle.

Inclusion Criteria:

• Stage IV breast cancer, stage IV NSCLC (Non-Small Cell Lung Cancer) (, stage IV sarcoma
• ECOG (Eastern Cooperative Oncology Group) PS (Performance Status) 0-2
• Measurable disease
• No more than 4 prior chemotherapeutic regimens for metastatic disease
• Patients must be >/= 18 years.
• Patients may not have received eribulin or lenvatinib previously
• Patients must have a life expectancy of greater than 12 weeks.
• Patients may have had a prior diagnosis of cancer if it has been > 5 years since their last treatment and are considered free of disease.
• Patients must have normal organ and marrow function as defined below:

Leukocytes ≥ 3,000/uL Absolute neutrophil count ≥ 1,500/uL Platelets ≥ 100,000/uL Child Pugh score ≤ 10 Patients must be able to swallow and retain oral medication. All patients must have given signed, informed consent prior to registration on study.

Exclusion Criteria:

• Women who are pregnant or lactating are not eligible for study treatment.

• Patients who are undergoing concomitant radiotherapy are NOT eligible for participation.

• Patients who are receiving any other investigational agents or concurrent anticancer therapy are NOT eligible for participation. Previous systemic treatment and/or radiation therapy is allowed with a 14 day washout period prior to registration.

• Lesions that have been radiated previously cannot be considered target lesions

• Prior treatment related side effects must have resolved to < Grade 2 severity per Common Terminology Criteria for Adverse Events (CTCAE version 4.03), except alopecia and infertility.

• Patients who are taking any herbal (alternative) medicines are NOT eligible for participation. Patients must be off any such medications by the time of registration.

• Patients with known brain metastases are NOT eligible for participation unless the brain metastases are treated (either with surgical excision, stereotactic radiosurgery or radiotherapy) and have been stable for at least 4 wks per MR performed, the patient is asymptomatic and has discontinued corticosteroids if taken for that purpose.

• Patients with any of the following conditions or complications are NOT eligible for participation:

  1. GI tract disease resulting in an inability to take oral medication
  2. Malabsorption syndrome
  3. Require IV alimentation
  4. History of prior surgical procedures affecting absorption
  5. Uncontrolled inflammatory GI disease (e.g., Crohn's, ulcerative colitis).
  6. Hypersensitivity of any of the components of eribulin or lenvatinib
  7. History of significant neurological ( no neuropathy more than grade 2) or psychiatric disorders
  8. Significant non neoplastic liver disease (Cirrhosis, active chronic hepatitis)
  9. Immunocompromised subjects, including patients with human immunodeficiency virus
  10. Significant non neoplastic renal disease
  11. Active infection requiring systemic therapy.
  12. Significant cardiovascular impairment: history of congestive heart failure greater than New York Heart Association (NYHA) Class II, uncontrolled arterial hypertension, unstable angina, myocardial infarction or stroke within 6 months of the first dose of study drug; or cardiac arrhythmia requiring medical treatment
  13. Prolongation of QTc interval to more than 480 milliseconds when electrolyte balance is normal
  14. Major surgery within 4 weeks prior to first dose of the study drug.

Adverse events were collected for all subjects from first cycle of the administration of the study drug through the end of the active study follow-up of the study during treatment up to 50 months. No subjects were escalated to a higher dose due to toxicity concerns, so all participants received the same dose.