TSN222 in Subjects With Advanced Solid Tumors or Lymphomas

Inclusion Criteria: Subjects must meet all the following inclusion criteria to be eligible for participation in this study: 1. The subject fully understands the requirements of the study and voluntarily signs the ICF. 2. At least 18 years of age at the time of informed consent. 3. Life expectancy of 3 months or more. 4. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. 5. Willing to provide tumor tissues and accept tumor biopsies during study. 6. 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. 7. 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. Exclusion Criteria: Subjects will be excluded if they meet any of the following criteria: 1. Untreated or symptomatic central nervous system (CNS) metastases. Note: Subjects with asymptomatic treated CNS metastases are eligible provided they have been clinically stable and not requiring steroid for at least 4 weeks following CNS directed therapy are eligible for study entry. 2. Prior history of active malignant disease other than that being treated in this study. Exceptions: malignancies that were treated curatively and have not recurred within the past 5 years (i.e., completely resected basal cell carcinoma and squamous cell carcinoma of the skin; and completely resected carcinoma in situ of any type) (only applicable to phase 2 part). 3. Any unresolved Grade 2 or higher toxicity from previous anticancer therapy except alopecia and grade 2 peripheral neuropathy. 4. Prior systemic anti-cancer treatment (chemotherapy, biologic therapy, or targeted therapy or herbal medicine) within 3 weeks or 5 half-lives (whichever is shorter) prior to the first dose of study drug; or prior systemic anti-tumor immunotherapy within 4 weeks or 5 half-lives (whichever is shorter) prior to the first dose of study drug. 5. Radical radiation within 4 weeks prior to the first dose of study drug; palliative radiotherapy to a non-target lesion within 2 weeks prior to the first dose of study drug. 6. Has participated in a study of an investigational agent and received study therapy or used an investigation device within 4 weeks prior to the first dose of study drug. 7. Major surgery within 4 weeks prior to first dose of study drug. 8. Severe infection within 4 weeks prior to the first dose of study drug, active infection requiring oral or intravenous antibiotics within 2 weeks prior to the first dose of study drug. 9. Active viral hepatitis. 10. History of human immunodeficiency virus (HIV) infection. 11. Known interstitial lung disease history, or current active pneumonitis, radiation pneumonitis requiring hormonal therapy, or uncontrolled lung disease. 12. Symptomatic uncontrolled effusion in body cavities (e.g., pleural effusion, ascites and pericardial effusion). 13. History of significant bleeding event (\> 30ml) within 3 months before the first dosing or hemoptysis (\> 2.5 mL of bright red blood or at least 0.5 teaspoon per episode) within 4 weeks before the first dosing； 14. Severe cardiovascular disease within 6 months of the first dose including cerebrovascular accident, transient ischemic attack, myocardial infarction, or unstable angina, New York Heart Association (NYHA) class III or IV heart failure or uncontrolled arrhythmia. 15. Uncontrolled hypertension (systolic pressure \>150mmHg or diastolic pressure \> 90mmHg). 16. Has the average corrected QT interval by Fridericia's formula (QTcF) prolongation to \> 480 millisecond (ms) based on 12-lead electrocardiograph (ECG) in triplicate, or with a history of additional risk factors for torsade de pointes (e.g., heart failure, hypokalemia, family history of long QT syndrome or unexplained sudden death under 40 years of age in first degree relatives). 17. Severe gastrointestinal disease, including but not limited to: * Peptic ulcer disease in the past 3 months prior to the first dosing. * Clinically significant gastrointestinal bleeding as evidenced by hematemesis, hematochezia, or melena in the past 3 months prior to the first dosing without evidence of resolution documented by endoscopy or colonoscopy. * Active colitis requiring ongoing treatment within 4 weeks prior to the first dosing, including infectious colitis, radiation colitis and ischemic colitis. * History of ulcerative colitis or Crohn's disease. 18. Active autoimmune diseases or history of autoimmune diseases that may relapse, or high-risk conditions (e.g., prior allogeneic hematopoietic stem cell transplantation or organ transplantation that requires immunosuppression), with the following exceptions: controlled type 1 diabetes, autoimmune hypothyroidism (provided it is managed with hormone replacement therapy only). 19. Any condition that required systemic treatment with either corticosteroids (\> 10 mg daily of prednisone or equivalent) or other immunosuppressive medication ≤ 14 days before the first dose of investigational product, with the following exceptions: * Topical, ocular, intra articular, intranasal, or inhalational corticosteroid with minimal systemic absorption. * Short course (≤ 7 days) of corticosteroid prescribed prophylactically (e.g., for contrast dye allergy) or for the treatment of a non-autoimmune condition (e.g., delayed-type hypersensitivity reaction caused by contact allergen). 20. Receipt of any live vaccines within 4 weeks prior to first dose of study drug. 21. Females who are pregnant or nursing. 22. Has a history or current evidence of any severe condition, concurrent therapy, or laboratory abnormality that might confound the interpretation of the study results, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the investigator.