Combination of a HER2-targeting vaccine and immunotherapy for advanced endometrial cancer

* INCLUSION CRITERIA:
* Histologically confirmed endometrial cancer.
* Radiographically confirmed metastatic or locally advanced disease.
* Evaluable (measurable or non-measurable) disease, per RECIST 1.1.
* HER2 IHC 1+, 2+ or 3+ tumor confirmed by PATHWAY HER2 (4B5) test. NOTE: The HER2 status in participants who had prior anti-HER2 therapy should be confirmed in the tumor tissue obtained after completing the anti-HER2 therapy.
* Participants must have received and progressed after at least one (1) line of systemic therapy for endometrial cancer.
* Age \>=18 years.
* ECOG performance status \<=2.
* Participants must have available tumor tissue or be willing to undergo a mandatory research biopsy. NOTE: Samples must be collected after HER2 directed therapy if the participant had anti-HER2 therapy.
* Participants must have adequate organ and marrow function as defined below:

  * Absolute neutrophil count (ANC) \> 1,000/microliter
  * Platelets \> 100,000/microliter
  * Hemoglobin (Hgb) \> 9 g/dL (any number of transfusions within 60 days before apheresis is allowed)
  * Total bilirubin \<=1.5 X upper limit of normal (ULN). NOTE: In participants with Gilbert s Syndrome or known liver metastasis, total bilirubin \<=3.0 X ULN is allowed
  * Aspartate aminotransferase (AST) / Alanine aminotransferase (ALT) \<=3.0 X ULN. NOTE: AST/ALT \<=5.0 X ULN is allowed in participants with known liver metastasis
  * An estimated creatinine clearance (CrCl) \<=1.5 X ULN OR \>30 mL/min/1.73 m2 for participants with creatinine levels \>1.5 X ULN (calculated creatinine clearance (CrCl) (eGFR may also be used in place of CrCl)
  * Dip stick urine protein \< 3 or urine protein \< 1 gram (g)/24 hour if dip stick urine is \>= 3+
* Hepatitis B virus (HBV)-infected participants can be enrolled if HBV DNA is undetectable. Hepatitis C virus (HCV)-infected participants can be enrolled if HCV RNA level is undetectable.
* Participants with previously treated non-active brain metastases or central nervous system metastases more than 28 days from definitive radiotherapy or surgery are eligible.
* Individuals of child-bearing potential (IOCBP) must agree to use highly effective contraception (hormonal, intrauterine device (IUD), tube ligation, a partner has had the previous vasectomy, abstinence) at the time of study entry, for the duration of study treatment, and up to 6 months after the last dose of the study drug(s).
* Nursing participants must be willing to discontinue nursing from study treatment initiation through 6 months after the last dose of the study drug(s).
* Participants must be able to understand and be willing to sign a written informed consent document.

EXCLUSION CRITERIA

* Administration of any standard of care or investigational checkpoint inhibitors (e.g., anti-CTLA, anti-PD-1, anti-PD-L1, anti-TIGIT, anti-TIM3, or anti-LAG3 antibodies or small molecules) within 6 months prior to apheresis.
* History of grade 3 or 4 immune related adverse events from the use of immune checkpoint inhibitors.
* History of Lenvatinib use
* History of severe immediate hypersensitivity reaction to compounds similar to study drugs or their components (e.g., monoclonal antibody preparations).
* Surgery to abdomen/pelvis/chest within 3 months prior to apheresis.
* Other malignancies diagnosed within 24 months prior to apheresis. NOTE: Participants who completed treatment for in-situ carcinomas (e.g., breast, cervix, bladder), or basal or squamous cell carcinoma of the skin are eligible if no ongoing treatment is needed per Standard of Care.
* Arterial or venous thromboembolism within 6 months prior to apheresis.
* History of cerebrovascular accident or stroke (transient ischemic attack, hemorrhagic or ischemic) within 6 months prior to apheresis.
* Functional or objective cardiac dysfunction: New York Heart Association (NYHA) Functional Capacity III or IV or Objective Assessment C or D.
* Fridericia's corrected QT interval (QTcF) \>= 480 msec or evidence of third-degree AV block on screening electrocardiogram (ECG).
* Ejection fraction by screening echocardiogram \< 50 percent.
* Participants requiring therapeutic anticoagulation regimen(s) (e.g., warfarin, rivaroxaban, apixaban, dabigatran, edoxaban, low molecular weight heparin \[e.g., enoxaparin, dalteparin, tinzaparin\], heparin, fondaparinux).
* History of gastrointestinal or non-gastrointestinal fistula \>= Grade 3 (CTCAE v.5.0).
* Radiographic evidence of major blood vessel invasion/infiltration.
* History of hemoptysis or tumor bleeding within 1 month prior to apheresis.
* Current gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib.
* Any form of primary immunodeficiency.
* Participants with active autoimmune disease or a history of autoimmune disease, which require immune suppressive treatment such as systemic corticosteroids or other systemic immune suppressants (e.g., methotrexate, cyclosporine, and biologics). NOTE: Participants with vitiligo, endocrine deficiencies on replacement dose are eligible.
* Systemic corticosteroid therapy of higher than a physiologic dose (the equivalent of prednisone 10 mg/day) within 14 days prior to apheresis. NOTE: Any topical steroid medications (e.g., corticosteroid creams, ointments, and eye drops) are allowed.
* Solid organ or allogeneic hematopoietic stem cell transplant recipients.
* Human immunodeficiency virus (HIV)-positive participants.
* Pregnancy (confirmed with beta-Human chorionic gonadotropin (HCG) serum or urine pregnancy test performed in IOCBP at screening).
* Uncontrolled intercurrent illness or situation that would limit compliance with study requirements.