FT500 is an off-the-shelf, iPSC-derived NK cell product that can bridge innate and adaptive immunity, and has the potential to overcome multiple mechanisms of immune checkpoint inhibitor (ICI) resistance. The preclinical data provide compelling evidence supporting the clinical investigation of FT500 as monotherapy and in combination with ICI in participants with advanced solid tumors.

Inclusion Criteria:

1. Diagnosis of the following, as per Regimen Cohort:

1A. Regimen A: FT500 Monotherapy (Dose Escalation): An advanced solid tumor malignancy, including lymphoma, in a participant who has failed or refused available FDA-approved therapies and is now a candidate for salvage therapy.

1B. Regimen B and BB (Dose Escalation): FT500 (+ IL-2, Regimen BB only) + ICI: An advanced solid tumor malignancy, including lymphomas, that has progressed on treatment with at least one ICI (ie, nivolumab, pembrolizumab or atezolizumab), in a participant who has also failed or refused other available approved therapies and is now a candidate for salvage therapy.

1C. Regimen B(Dose Expansion): FT500 (+ IL-2, Regimen BB only) + ICI An advanced solid tumor malignancy or lymphoma in a participant with disease relapse or progression on an ICI (nivolumab, pembrolizumab, or atezolizumab) in an approved indication per the respective USPI.

2. Willingness to provide informed consent as described in the protocol, which includes compliance with the requirements and restrictions listed in the ICF and in this protocol.

3. Age >18 years old at the time of signing the ICF. 4. Presence of measurable disease by iRECIST or RECIL criteria, assessed before the start of lympho-conditioning and within 28 days prior to Day 1.

5. Contraceptive use by women or men should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies.

5a. Female participants: Women of childbearing potential (WOCBP) must use a highly effective form of contraception from the screening visit until at least 12 months after the final dose of CY, at least 4 months after the final dose of FT500, at least 4 months after the final dose of pembrolizumab, and at least 5 months after the final dose of nivolumab or atezolizumab, whichever is latest.

5b. Male participants: Males must be sterile (biologically or surgically) or use a highly effective method of contraception from the screening visit until at least 14 months after the final dose of CY, at least 6 months after the final dose of FT500, at least 6 months after the final dose of pembrolizumab, and at least 7 months after the final dose of nivolumab or atezolizumab, whichever is latest.

6. Willingness to comply with study procedures through the planned study duration. For patients with >1 measurable lesion, agreement to undergo a biopsy from a safely accessible site per Investigator assessment for exploratory biomarker assessments.

7. Provision of signed and dated ICF to agree to participate, at time of withdrawal or completion of this study, in Fate Therapeutics' long-term, non-interventional, observational study, FT-003.

Exclusion Criteria:

All participants:

1. Females who are pregnant or breastfeeding. 2. ECOG performance status ≥ 2. 3. Evidence of insufficient organ function as determined by any one of the following: 3a. Neutrophils <1000/µL or platelets <75,000/µL. 3b. Estimated creatinine clearance <50 mL/minute (Cockcroft-gault). 3c. Total bilirubin >2 x upper limit normal (ULN) with the exception of participants with Gilbert's Syndrome or known liver metastases.

3d. Aspartate aminotransferase (AST) >3 x ULN, or alanine aminotransferase (ALT) >3 x ULN. For participants with known liver metastases, AST or ALT >5 x ULN.

3e. Oxygen saturation <90% on room air. 3f. Left ventricular ejection fraction (LVEF) <40% (eg by echocardiogram (ECHO) or multi-gated acquisition (MUGA) scan).

4.Receipt of any biological therapy, chemotherapy, or radiation (except palliative radiation) within 2 weeks prior to Day 1. Participants in Regimen B currently taking an ICI must interrupt ICI dosing at least 2 weeks prior to Day 1.

5. CNS metastases that have not been treated; or treated CNS metastases that have not been stable for at least 4 weeks.

6. Clinically significant cardiovascular disease, including stroke or myocardial infarction within 6 months prior to first study medication; or the presence of unstable angina or congestive heart failure of New York Heart Association grade 2 or higher.

7. Currently receiving or likely to require systemic immunosuppressive therapy (eg, prednisone >5 mg daily) for any reason from Day -7 to Day 29.

8. Uncontrolled infections. 9. Known allergy to the following FT500 components: Albumin (Human) or DMSO. 10. Presence of any medical or social issues that are likely to interfere with study conduct, or may cause increased risk to participant.

11. Any medical condition or clinical laboratory abnormality that, per Investigator or Medical Monitor judgement, precludes safe participation in and completion of the study, or that could affect compliance with protocol conduct or interpretation of results. Participants who have had prior receipt of a Fate Therapeutics investigational human iPSC product may be eligible for the study with approval from the Medical Monitor.

Additional Exclusion Criteria for Regimen B: FT500 + ICI:

11. Participants who experienced an ICI-related adverse reaction that resulted in discontinuation of the ICI.

12. Presence or history of autoimmune disease (eg, lupus erythematosus, rheumatoid arthritis, Addison's disease, autoimmune disease associated with lymphoma, Crohn's disease, ulcerative colitis), except for participants with isolated vitiligo, atopic dermatitis, controlled hypoadrenalism or hypopituitarism, and controlled thyroid disease.

13. Participants who have received an allograft organ transplant.