The primary purpose of this research study is to see whether adding bavituximab (an investigational drug) to durvalumab will improve the results of the treatment for non-small-cell lung cancer.

Inclusion Criteria:

• Signed Written Informed Consent
• Male or female at least 18 years of age
• Histologically or cytologically documented NSCLC (Non-small-cell lung carcinoma) who present with Stage IV disease (according to the American Joint Committee on Cancer Staging Manual [7th edition]) or with recurrent disease or progressive disease following multimodal therapy (radiation therapy, surgical resection, or definitive chemoradiation therapy for locally advanced disease)
• Disease recurrence or progression during or after one prior platinum-based doublet chemotherapy treatment for advanced or metastatic disease
• Measurable disease on cross-sectional imaging per RECIST 1.1
• Eastern Cooperative Oncology Group performance status 0 or 1
• Tumor tissue (archival or recent tumor biopsy) must be available for biomarker evaluation
• Adequate hematologic function (absolute neutrophil count ≥1500 cells/µL; hemoglobin ≥9 g/dL; platelets ≥100,000/µL).
• Serum creatinine CL>40 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection for determination of creatinine clearance
• Adequate hepatic function (serum bilirubin ≤1.5 × ULN, serum albumin levels ≥3.0 g/dL, alanine aminotransferase [ALT] ≤2.5 × ULN, and aspartate aminotransferase [AST] ≤2.5 × ULN)
• Female patients must either be of nonreproductive potential or must have a negative serum pregnancy test upon study entry
• All patients of reproductive potential (ie, not surgically sterile or postmenopausal) must agree to use a highly effective method of contraception during and 90 days after the end of study treatment

Exclusion Criteria:

• Known history of bleeding diathesis or coagulopathy (von Willebrand disease or hemophilia)
• Tumors invading large blood vessels that, in the opinion of the Investigator, put the patient at risk for major hemorrhage
• Clinically significant bleeding, such as gross hematuria, gastrointestinal bleeding, and hemoptysis within the 6 months before screening, unless the cause has been identified and adequately treated (eg, cystitis, ulcer)
• Thromboembolic events (eg, deep vein thrombosis, pulmonary embolism, arterial thrombosis) within 6 months before screening
• Symptomatic coronary artery disease, cerebrovascular accident, transient ischemic attack, myocardial infarction, arterial embolism, or unstable angina pectoris within 6 months prior to screening
• QT interval using Fridericia's Correction (QTc) > 500 ms
• Symptomatic or clinically active brain metastases. Patients are eligible if brain metastases are adequately treated. Patients must be either off corticosteroids or on a stable or decreasing dose of ≤10 mg of daily prednisone (or equivalent).
• Patients with symptomatic interstitial lung disease or inflammatory pneumonitis that may interfere with the detection or management of suspected drug-related pulmonary toxicity
• Other active malignancy requiring concurrent intervention.
• Acute toxicities attributed to prior anti-cancer therapy other than alopecia and fatigue must have resolved to Grade 1 or baseline before administration of study drug
• Active or prior documented autoimmune disease within the past 2 years
• Current or prior use of immunosuppressive medication within 28 days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid
• Active or prior documented inflammatory bowel disease (eg, Crohn's disease, ulcerative colitis)
• History of primary immunodeficiency
• History of allogeneic organ transplant
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active bleeding diatheses including any subject known to have evidence of acute or chronic hepatitis B, hepatitis C or human immunodeficiency virus (HIV), or psychiatric illness/social situations that would limit compliance with study requirements or compromise the ability of the patient to give written informed consent
• Previous clinical diagnosis of tuberculosis
• History of hypersensitivity to any of the excipients of bavituximab and durvalumab including polysorbate-80-containing infusions.
• Serious nonhealing wound, including wound healing by secondary intention
• Major surgery within 4 weeks prior to Cycle 1 Day 1 (C1D1)
• Receipt of live attenuated vaccination within 30 days prior to study entry or within 30 days of receiving durvalumab
• Prior therapy with a PD-1 or PD-L1 inhibitor, including durvalumab.
• Prior therapy with bavituximab.
• Investigational therapy within 28 days prior to C1D1.
• Patient has a condition or is in a situation which, in the Investigator's opinion, may put the patient at significant risk, may confound the study results, or may interfere significantly with the patient's participation in the study