Lenvatinib, Pembrolizumab, and Paclitaxel for Treatment of Recurrent Endometrial, Epithelial Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Participants who are at least 18 years of age on the day of signing informed consent will be enrolled in this study * Women with histologically confirmed endometrial cancer, epithelial ovarian cancer, fallopian tube cancer or primary peritoneal cancer (all histological subtypes) * Patients must have received prior treatment with a platinum containing regimen and may have received 1-3 prior regimens. Hormonal therapy and maintenance therapy (with bevacizumab or PARP inhibitor) does not count towards the number of prior treatments * Patients with ovarian, fallopian tube or primary peritoneal cancer must be platinum resistant (progression \< 6 months after completion of a platinum containing regimen) or not a candidate for further platinum treatment * Patients with and without mismatch repair deficiency are allowed * Prior PD-1/PD-L1 inhibitors are allowed as long as this was not the most recent regimen and treatment was not discontinued due to side effects/toxicity. Prior weekly paclitaxel is allowed as long as this was not the most recent regimen and treatment was not discontinued due to side effects/toxicity * Prior targeted therapy targeting angiogenesis is allowed as long as treatment was not discontinued due to side effects/toxicity * Have measurable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions * A female participant is eligible to particip…