• Participants are eligible to be included in the study only if all the following criteria apply:

• Female participants who are at least 18 years of age on the day of signing informed consent.

• Histologically confirmed diagnosis of squamous, adenocarcinoma or adenosquamous cervical cancer, that is recurrent or metastatic.

• Prior therapy: May have received up to 2 prior lines of systemic chemotherapy in the setting of advanced, metastatic (Stage IVB) or recurrent cervical cancer. May have received prior checkpoint inhibitor for advanced, metastatic (Stage IVB) or recurrent cervical cancer. May have received prior bevacizumab or antiangiogenic agent for recurrent or metastatic cervical cancer,

• Include whether prior checkpoint inhibitor was used in first line setting or second line setting.

• Prior Radiation therapy will be allowed and not counted as a line of treatment.

• Prior chemotherapy used as radiation sensitizer (e.g. cisplatin) used as treatment during chemoradiation will be allowed and counted as a line of treatment.

• Female participants:

‣ A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies:

⁃ Not a woman of childbearing potential (WOCBP)

• OR

• Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), with low user dependency, or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis), during the intervention period and for at least 120 days post pembrolizumab or 30 days post lenvatinib whichever occurs last. The investigator should evaluate the potential for contraceptive method failure (i.e., noncompliance, recently initiated) in relationship to the first dose of study intervention.

⁃ A WOCBP must have a negative highly sensitive pregnancy test (urine or serum as required by local regulations) within 24 hours before the first dose of study intervention.

⁃ If a urine test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive.

⁃ The investigator is responsible for review of medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a woman with an early undetected pregnancy.

• Participants must have a PD-L1 diagnostic test of primary or recurrent archival tumor tissue.

• Participants may have progressed on treatment with an anti-PD-1/L1 mAb administered either as monotherapy or in combination with other checkpoint inhibitors or other therapies. PD-1 treatment progression is defined by meeting all the following criteria:

∙ Has received at least 2 doses of an approved anti-PD-1/L1 mAb.

‣ Has demonstrated disease progression after anti-PD-1/L1 as defined by RECIST v1.1. The initial evidence of PD is to be confirmed by a second assessment no less than 4 weeks from the date of the first documented disease progression, in the absence of rapid clinical progression.

‣ Progressive disease has been documented within 12 weeks from the last dose of anti-PD-1/L1 mAb.

• i. Progressive disease is determined according to iRECIST.

• ii. This determination is made by the investigator. Once disease progression is confirmed, the initial date of disease progression documentation will be considered the date of disease progression.

⁃ Participants who have AEs due to previous anticancer therapies must have recovered to ≤Grade 1 or baseline. Participants with endocrine-related AEs who are adequately treated with hormone replacement or participants who have ≤Grade 2 neuropathy are eligible.

⁃ The participant (or legally acceptable representative if applicable) provides written informed consent for the trial.

⁃ 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.

⁃ Archival tumor tissue sample or newly obtained \[core, incisional or excisional\] biopsy of a tumor lesion not previously irradiated has been provided. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue.

⁃ Have an Eastern Cooperative Oncology Group performance status of 0 to 1. Evaluation of ECOG is to be performed within 7 days prior to the first dose of study intervention.

⁃ Have adequate organ and marrow function as defined in the following table (Table 2). Specimens must be collected within 10 days prior to the start of study intervention.

⁃ Criteria for known Hepatitis B and C positive subjects.

⁃ Hepatitis B and C screening tests are not required unless:

‣ Known history of HBV or HCV infection

‣ As mandated by local health authority

⁃ Hepatitis B positive subjects

∙ Participants who are HBsAg positive are eligible if they have received HBV antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to randomization.

‣ Participants should remain on anti-viral therapy throughout study intervention and follow local guidelines for HBV anti-viral therapy post completion of study intervention.

⁃ Participants with history of HCV infection are eligible if HCV viral load is undetectable at screening.

⁃ \- Participants must have completed curative anti-viral therapy at least 4 weeks prior to randomization.

⁃ Have adequately controlled BP with or without antihypertensive medications, defined as BP ≤150/90 mmHg with no change in antihypertensive medications within 1 week prior to randomization.

⁃ Ability to understand and the willingness to sign a written informed consent.