• Aged \>=18 years

• For Dose-Escalation: Females (TNBC, EC and OC) or males/females (NSCLC, adenocarcinoma). Participants with the following disease characteristics:

• Participants with the following tumor types, each as a separate arm:

‣ TNBC: Histologically confirmed diagnosis of metastatic TNBC (that is, estrogen receptor (ER) negative/progesterone receptor negative/ human epidermal growth factor receptor 2 (HER2) negative (defined as immunohistochemistry (IHC) less than (\<) 2 plus (+) or fluorescence in situ hybridization (FISH) negative) breast cancer). Previously treated with at least one line of systemic anticancer therapy (cytotoxic or targeted anticancer agents) in the metastatic setting.

‣ NSCLC adenocarcinoma: Histologically or cytologically confirmed metastatic NSCLC adenocarcinoma: participants who have failed previous treatment for metastatic disease, are not indicated or failed epidermal growth factor receptor (EGFR)-, Anaplastic lymphoma kinase (ALK) -, B-Raf proto-oncogene (BRAF) - or c-ros oncogene 1 (ROS1) - targeted therapy, and for whom no alternative standard therapy exists.

‣ EC: Histologically confirmed diagnosis of advanced, recurrent or metastatic EC. Relapsed or failure of at least one platinum-based regimen or one immunotherapy-based regimen.

‣ OC or primary peritoneal cancer or fallopian tube cancer: Histologically confirmed diagnosis of high grade serous epithelial ovarian cancer or primary peritoneal cancer or fallopian tube cancer.

• Participants must have:

⁃ platinum-resistant disease (defined as progression within 6 months after the last dose of at least 4 cycles of the last platinum containing chemotherapy regimen)

⁃ received up to 4 lines of systemic therapy post development of platinum resistance.

• For Dose-Confirmation and Dose Optimization:

• Note: Only participants with histologically confirmed diagnosis of advanced, recurrent, or metastatic EC will be enrolled at sites in France.

• High-grade serous ovarian cancer or primary peritoneal cancer or fallopian tube cancer:

⁃ Platinum-resistant disease:

• For participant with 1 line of platinum-containing therapy: progression greater than (\>) 1 month and less than or equal to (\<=) 6 months after the last dose of the first platinum-containing chemotherapy regimen (of at least 4 cycles)

∙ For participant with 2-3 lines of platinum-containing therapy: progression during or within 6 months after the last dose of the 2nd or 3rd platinum-containing chemotherapy regimen.

⁃ Have received up to 3 prior lines of systemic therapy and for whom single-agent therapy is appropriate as the next line of therapy. Participants may have been treated with up to one line of therapy subsequent to determination of platinum-resistance. In Dose Optimization Part B participants may have received up to 3 prior lines of systemic therapy, up to 4 prior lines is permitted for participants who have received prior mirvetuximab soravtansine

• Neoadjuvant plus/minus (±) adjuvant will be considered 1 line of therapy.

∙ Maintenance therapy (example, bevacizumab, PARP inhibitors) will be considered part of the preceding line of therapy (will not be counted as an independent line of therapy).

∙ Hormonal therapy will be counted as a separate line of therapy unless it was given as maintenance.

∙ Therapy changed due to toxicity in the absence of progression will be considered part of the same line.

• Endometrial cancer (not enrolled in Dose Optimization Part B):

⁃ Participants must have histologically confirmed diagnosis of advanced, recurrent, or metastatic EC. All histologic (including carcinosarcoma \[no more than one participant at any dose level\]) and molecular subtypes will be included. Participants may have been treated with an Immune Checkpoint Inhibitor (ICI) containing regimen (or be ineligible for ICI treatment) and must have had no more than 2 prior regimens (not including adjuvant therapy if progression or recurrent/metastatic disease occurred more than 6 months after the completion of the last cycle of adjuvant therapy).

⁃ Note: There is no restriction regarding prior hormonal therapy.

• Available tumor tissue for FRA expression percent (%) by IHC analysis as assessed at a central laboratory. There is no minimum requirement for FRA expression (%). However, the tumor sample must be evaluable for IHC analysis (that is, of sufficient quality with adequate tumor content). Sample resubmission will be permitted for participants with tissue result of non-evaluable who are otherwise eligible. Tumor sample submission must be archival formalinfixed, paraffin-embedded (FFPE) tissue block, or unstained slides sectioned within 45 days from the latest FFPE block, or a fresh biopsy sample obtained during screening but prior to initiation of study treatment. Participants who have received prior treatment with mirvetuximab soravtansine will be required to provide a fresh biopsy sample during screening.

• Radiological disease progression on or after the most recent therapy by investigator assessment.

• Measurable disease meeting the following criteria (confirmed by central radiographic review, in the Dose-Confirmation Part only):

‣ At least one lesion of \>1.0 centimeter (cm) in long axis diameter for non-lymph nodes or \>1.5 cm in short axis diameter for lymph nodes that is serially measurable according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 using either computed tomography (CT) or magnetic resonance imaging (MRI),

⁃ Lesions that have had external beam radiotherapy (EBRT) or loco-regional therapies such as radiofrequency (RF) ablation must show evidence of PD based on RECIST 1.1 to be deemed a target lesion.

• ECOG PS of 0 or 1.

• Participants who are expected to survive a minimum of 3 months after the first administration of the study drug.

• Adequate renal function as evidenced by serum creatinine less than or equal to (\<=) 1.5 milligram per deciliter (mg/dL) or calculated creatinine clearance \>=50 milliliter per (mL) /minute according to a 12 or 24 hour urine collection.

• For Dose Optimization Part B, adequate renal function as evidenced by calculated creatinine clearance \>=50 milliliters per minute (mL/min) by Cockcroft-Gault formula.

• Adequate bone marrow function, as evidenced by:

‣ Absolute neutrophil count (ANC) \>=1.0\*10\^9 per liter (/L) (MORAb-202 monotherapy cohorts only)

⁃ ANC \>=1.5\*10\^9/L (MORAb-202 plus lenvatinib cohorts)

⁃ Hemoglobin (Hgb) \>=9.0 gram per deciliter (g/dL)

⁃ Platelet count \>=75\*10\^9/L Growth factors or transfusions as per institutional practice, are allowed if needed to achieve the above values. Growth factor and platelet transfusion should not be used within 7 days of initiation of study treatment.

⁃ Adequate liver function, as evidenced by:

∙ Total bilirubin \<=1.5\*upper limit of normal (ULN) except for unconjugated hyperbilirubinemia (example, Gilbert's syndrome)

‣ Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<=3\*ULN (in the case of liver metastases \<=5\*ULN). Participants with Alkaline Phosphatase (ALP) \<=3\*ULN unless they and are known to have bone metastases in which case higher ALP values will also be allowed.

‣ Albumin \>3.0 g/dL.

⁃ Participants must undergo a washout period required from the end of prior treatment to the first administration of the study drug that will be as follows:

⁃ Prior anticancer therapy:

‣ Prior chemotherapy, surgical therapy, radiation therapy: \>3 weeks. Prior chest radiotherapy or pneumonectomy is an exclusion.

‣ Antibody and other biologic therapeutic agents: \>=4 weeks.

‣ Endocrine therapy or, small-molecule targeted therapy: \>2 weeks.

‣ Immunotherapy \>=4 weeks.

⁃ Participants with a history of deep vein thrombosis (DVT) within 3 months of enrollment must be on a stable dose of anticoagulation as demonstrated by appropriate laboratory parameters (depending on the anticoagulant agent) for a minimum of 2 weeks before to starting study treatment. Anticoagulation must continue while on study treatment.

⁃ Participants at risk for DVT secondary to central venous catheters or with past medical history of DVT or clinical symptoms suggestive of DVT must have venous Doppler ultrasonography to rule out DVT during the screening period and before to initiation of study treatment.

⁃ If a participant has undergone major surgery, the participant must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment.

⁃ Resolution of anticancer therapy-related or radiation-related toxicities to Grade 1 severity or lower, except for stable sensory neuropathy (Grade \<=2), anemia (\[haemoglobin\] Hgb \>=9.0 g/dL), and alopecia (any grade).

⁃ Participant must be willing and able to comply with all aspects of the protocol.

⁃ Participant must provide written informed consent prior to any study-specific screening procedures.

⁃ For cohorts where MORAb-202 is used in combination with lenvatinib: Has adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP \<=150/90 millimeter of mercury (mm Hg) and no change in antihypertensive medications within 1 week before the first administration of the study drug.