⁃ Subjects must meet all the following inclusion criteria to be eligible for participation in this study:

• The subject fully understands the requirements of the study and voluntarily signs the ICF.

• At least 18 years of age at the time of informed consent.

• Life expectancy of 3 months or more.

• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1.

• Willing to provide tumor tissues and accept tumor biopsies during study.

• At least one measurable tumor lesion per RECIST v1.1 or Lugano 2014 response criteria (only applicable for phase 2); note: the measurable lesions should be non-injected and non-biopsied during study.

• Subjects must meet the following criteria for each of the respective parts of the study

⁃ Phase 1 part:

⁃ Has a pathologically documented unresectable locally advanced or metastatic solid tumor or lymphoma that is refractory to or intolerable with standard treatment, or for which no standard treatment is available.

⁃ Phase 2 part:

⁃ Cohort 1: Has pathologically confirmed diagnosis of unresectable locally advanced or metastatic HNSCC that is considered incurable by local therapies, and is refractory to or intolerable with at least one systemic treatment in the advanced setting.

⁃ Cohort 2: Has pathologically confirmed diagnosis of unresectable locally advanced or metastatic melanoma that is refractory to or intolerable with at least prior two systemic treatments in the advanced setting for BRAF mutant subjects, or at least one systemic treatment in the advanced setting for BRAF non-mutant subjects.

⁃ Cohort 3: Has pathologically confirmed diagnosis of unresectable locally advanced or metastatic other solid tumors or lymphomas that is refractory to or intolerable with at least one systemic treatment in the advanced setting, or for which no standard treatment is available.

⁃ 9\. Adequate bone marrow function: 10. Adequate renal function: estimated creatinine clearance ≥ 50 mL/min as calculated using Cockcroft-Gault formula.

⁃ 11\. Adequate liver function: 12. Blood albumin ≥ 30g/L. 13. Adequate coagulation function: 14. Women of childbearing potential (WOCBP) and men must agree to follow instructions for method(s) of contraception during the treatment period and for at least 6 months after the last dose of TNS222. Contraception methods should be consistent with local regulations. Refer to Appendix 6 for details and definitions of WOCBP, postmenopausal females and contraception guidance.