* History of germline BRCA1-Associated Protein-1 (BAP1) mutations.
* Histologically confirmed by NCI Laboratory of Pathology (LP) subclinical/early-stage mesotheliomas.
* Participants with other early-stage BAP1-associated malignancies in addition to subclinical, early-stage mesotheliomas are eligible for the study.
* The extent of the disease (Tx by clinical staging criteria) must be insufficient to warrant approved front-line standard of care (SOC) therapies (surgery, chemotherapy, immunotherapy). Participants with clinical T1 tumors are eligible for protocol if they have been offered and have refused front-line SOC therapy.
* Evaluable disease as confirmed by minimally invasive (videoscopic) assessment (thoracoscopy and/or laparoscopy with biopsy).
* Willingness to undergo pre- and post-treatment minimally invasive thoracoscopy and/orlaparoscopy to assess treatment response.
* Willingness to co-enroll on 20-C-0106 (Prospective Evaluation of High Resolution Dual Energy Computed Tomographic Imaging, Noninvasive (Liquid) Biopsies, and Minimally Invasive Surgical Surveillance for Early Detection of Mesotheliomas in Patients with BAP1 Tumor Predisposition Syndrome) and 06-C-0014 (Prospective Evaluation of Genetic and Epigenetic Alterations in Patients with Thoracic) to enable collection/processing of tumor, blood and normal pleura).
* ECOG performance status <=1
* Adequate pulmonary reserve evidenced by forced expiratory volume (FEV)1 and diffusing capacity of the lungs for carbon monoxide (DLCO) >=35% predicted on screening pulmonary function testing (PFTs).
* Oxygen saturation >=92% on room air by pulse oximetry at screening.
* Adequate renal, hepatic, and hematopoietic function as defined below:
* leukocytes >= 3,000/micro L
* absolute neutrophil count >=1,500/micro L (without transfusion or cytokine support within 2 months prior to study treatment initiation)
* absolute lymphocyte count > 800/micro L
* platelets >= 100,000/micro L and < 1,200,000/micro L
* prothrombin time (PT) no more than 2 seconds above the upper limit of normal (ULN)
* total bilirubin < 1.5 X institutional ULN OR direct bilirubin <= 1 ULN for participants with total bilirubin >= 1.5 ULN serum albumin >=2.0 mg/dL
* aspartate aminotransferase (AST) <=2.5 X institutional ULN
* alanine aminotransferase (ALT) <= 2.5 X institutional ULN
* estimated glomerular filtration rate (eGFR) >=60 mL/min/1.73 m2.
* Individuals of child-bearing potential (IOCBP) and those able to father a child must agree to use an effective method of contraception (barrier, hormonal, intrauterine device (IUD), surgical sterilization) from the study entry and up to 3 months after the last dose of APG-115.
* Nursing (i.e., breastfeeding/chest feeding) participants must be willing to discontinue nursing from study treatment initiation through 4 weeks after the last dose of the study drug.
* The ability of a participant to understand and the willingness to sign a written informed consent document.