A Study to Evaluate the Safety and Pharmacology of DNIB0600A in Participants With Platinum-Sensitive Ovarian Cancer or Non-Squamous Non-small Cell Lung Cancer

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) status of 0 or 1. * Histologically documented epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer that is platinum sensitive. * PSOC (i.e., epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer) with documented radiographic progression or relapse within 6 to 18 months of most recent platinum-based chemotherapy. * Female participants of childbearing potential must use effective contraception as defined by study protocol and cannot be pregnant or breastfeeding. NSCLC-specific Inclusion Criteria: * Histological documentation of incurable, locally advanced, or metastatic non-squamous * NSCLC that has progressed on prior treatment * Not more than 2 prior regimens in the metastatic setting, including one prior cytotoxic regimen and one prior non-cytotoxic regimen (prior treatment with adjuvant therapy within 6 months of recurrence is considered a treatment regimen in the metastatic setting). * For participants with a documented epidermal growth factor receptor (EGFR) mutation or anaplastic lymphoma kinase (ALK) rearrangement, one additional line of non-cytotoxic prior treatment will be permitted provided the therapy is a targeted agent against the EGFR mutation or ALK rearrangement. * For participants with lung cancer, centrally confirmed high expression of a sodium-dependent phosphate transporter (NaPi2b) by immunohistochemistry (IHC) is required (i.e., IHC 2+ or 3+). Exclusion Criteria: * Anti-tumor therapy of any kind or major surgery within 4 weeks prior to Day 1. * For ovarian cancer participants only, platinum-based chemotherapy within 6 months prior to Day 1. * For ovarian cancer participants only, platinum treatment with more than two platinum-based chemotherapy regiments or more than four anti-cancer regimens, overall, for the treatment of ovarian cancer. * Palliative radiation within 2 weeks prior to Day 1. * Toxicity (except alopecia and anorexia) from prior therapy or neuropathy of grades \> 1. * Evidence of any significant disease or condition that could affect compliance with the protocol or interpretation of results. * Known active infection (except fungal nail infections). * History of liver disease or human immunodeficiency virus (HIV). * Other malignancy within the last 5 years, except for adequately treated or controlled carcinoma in situ of the cervix or skin cancer or primary endometrial cancer of stage \</= 1B. * Untreated or active central nervous system (CNS) metastases. * Prior treatment with NaPi2b- targeted therapy. Bevacizumab-Specific Exclusion Criteria (for Participants in Second Ovarian Expansion Cohort Only): * Inadequately controlled hypertension or history of hypertensive crisis or encephalopathy. * History of heart problems or thrombosis within 6 months prior to study start. * History of stroke within 6 months prior to study enrollment. * History of significant vascular disease. * History of expectoration of blood within 1 month prior to study start or blood clotting problems. * Core biopsy or other minor surgical procedure within 7 days prior to study start * Serious and non-healing wound, active ulcer, or untreated bone fracture.