Topotecan and Bevacizumab in Treating Patients With Stage IIIB or Stage IV Non-Small Cell Lung Cancer That Did Not Respond to Previous Systemic Chemotherapy

Inclusion Criteria: * Patients must have histologically or cytologically confirmed non-small cell lung cancer (NSCLC). Patients with extrathoracic-only squamous cell NSCLC are eligible. Intrathoracic squamous cell carcinoma will not be eligible. Mixed tumors will be categorized by the predominant cell type unless small cell elements are present, in which case the patient is ineligible. * Disease that has failed one or more prior standard therapy and is no longer likely to respond to such therapy. * Prior systemic chemotherapy, immunotherapy, or biological therapy is allowed, except for prior use of Avastin and topotecan in combination. Patient must be at least 14 days from previous radiation or systemic therapy (at least 30 days for investigational agents) and have recovered from the acute toxic effects of the treatment prior to study enrollment. * Disease status must be measurable or evaluable as defined by Response Evaluation Criteria In Solid Tumors (RECIST criteria) * Eastern Cooperative Oncology Group (ECOG) Performance status of 0 or 1 * Age 18 years or greater * Adequate organ function within 14 days of study registration including the following: * Adequate bone marrow reserve: * absolute neutrophil count (ANC) \> or = to 1.5 x 10\^9/L, * platelets \>100 x 10\^9/L, * hemoglobin \> 9 g/dL * Hepatic: * bilirubin \<1.5 times the upper limit of normal (x ULN), * alkaline phosphatase (ALP), aspartate transaminase (AST) and alanine transaminase (ALT) \<3.0 x ULN (ALP, AST, and ALT \<5 x ULN is acceptable if liver has tumor involvement) * Renal: * serum creatinine \< 2.0 * urine dipstick for proteinuria \< 2+ (patients discovered to have ≥2+ proteinuria on dipstick urinalysis at baseline should undergo a 24 hour urine collection and must demonstrate ≤ 1g of protein in 24 hours to be eligible) * Coagulation: * International Normalized Ratio (INR) \< 1.5 * Partial thromboplastin time (PTT) \< the upper limits of normal (ULN) * Women of childbearing potential and sexually active males are required to use an effective method of contraception (ie, a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) during the study and for 3 months after the last dose of study drug. * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. Exclusion Criteria: * Pregnant (positive pregnancy test) or breast-feeding. Topotecan is pregnancy category D - clear evidence of risk in pregnancy; Avastin is pregnancy category C - risk in pregnancy cannot be ruled out. Pregnancy testing is not required for post-menopausal or surgically sterilized women * Known hypersensitivity to any component of Avastin (bevacizumab) * Inadequately controlled hypertension (defined as systolic blood pressure \> 150 and/or diastolic blood pressure \> 100 mmHg) * Any prior history of hypertensive crisis or hypertensive encephalopathy * New York Heart Association (NYHA) Grade II or greater congestive heart failure * History of myocardial infarction or unstable angina within 6 months prior to Day 1 * History of stroke or transient ischemic attack within 6 months prior to Day 1 * Known central nervous system (CNS) disease, except for treated brain metastasis. Treated brain metastases are defined as having no evidence of progression or hemorrhage after treatment and no ongoing requirement for dexamethasone, as ascertained by clinical examination and brain imaging (MRI or CT) during the screening period. Anticonvulsants (stable dose) are allowed. Treatment for brain metastases may include whole brain radiotherapy (WBRT), radiosurgery (RS; Gamma Knife, LINAC, or equivalent) or a combination as deemed appropriate by the treating physician. Patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to Day 1 will be excluded * Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to Day 1 * History of hemoptysis (≥ ½ teaspoon of bright red blood per episode) within 1 month prior to Day 1 * Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) * Active malignancy other than non-small cell lung cancer (NSCLC), treated superficial basal cell and superficial squamous (skin) cell, or carcinoma in situ of the cervix within last five years are allowed. * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 1 or anticipation of need for major surgical procedure during the course of the study * Core biopsy or other minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to Day 1 * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to Day 1 * Serious, non-healing wound, active ulcer, or untreated bone fracture * Inability to comply with study and/or follow-up procedures