A Study of PEP07 (Checkpoint Kinase 1 Inhibitor) in Patients With Advanced Cancer

Inclusion Criteria: 1. Must be ≥ 18 years of age. 2. Must have histological or cytological confirmation advanced hematologic malignancy including: * Relapsed or refractory AML (by the 5th edition of World Health Organization \[WHO\] classification of Hematolymphoid tumors) * OR Relapsed or refractory MCL and have received at least two prior lines of treatment, including chemoimmunotherapy and BTKi and at least 1 measurable site of disease according to Revised Response Criteria for Malignant Lymphoma. 3. Must have Eastern Cooperative Oncology Group (ECOG) Performance score of 0 to 2. 4. Must have adequate renal function as demonstrated by a calculated creatinine clearance ≥ 50 mL/min; determined via urine collection for 24-hour creatinine clearance or by the Cockcroft Gault formula. 5. Must have adequate liver function as demonstrated by: * aspartate aminotransferase (AST) ≤ 2.5 × ULN * alanine aminotransferase (ALT) ≤ 2.5 × ULN * bilirubin ≤ 1.5 × ULN (unless considered due to leukemic organ involvement. Patients with Gilbert's Syndrome may have had a bilirubin \> 1.5 × ULN per discussion between the PI or designee and sponsor) 6. Left ventricular ejection fraction (LVEF) ≥ 50% measured by multiple-gated acquisition (MUGA) or echocardiogram. 7. Previous AEs have been improved to baseline or Grade ≤ 1 NCI CTCAE v5.0. 8. Female patients with reproductive potential must have a negative serum pregnancy test 7 days prior to the administration of PEP07. 9. Patients will be required to have a Covid negative test either via reverse transcriptase polymerase chain reaction (RTPCR) or a rapid antigen test (RAT) test on Day -7/Day 1. 10. Provision of signed and dated informed consent form. Exclusion Criteria: 1. Pregnant or breastfeeding females 2. Females of childbearing potential and males whose partners are of childbearing potential who do not agree to the use of 2 forms of highly effective contraception during the treatment period and for 120 days after the last dose of PEP07. 3. Patients who have received anti-cancer therapy including chemotherapy, radiotherapy, hormonal, or any investigational therapy within 14 days or 5 half-lives (whichever is shorter), or immunotherapy within 30 days prior to the first dose of PEP07. Patients who have received hydroxyurea or dexamethasone at any time prior to the start of study treatment is an exception to this criterion. 4. Patients who have undergone allogeneic hematopoietic stem cell transplant (HSCT) within 60 days of PEP07 treatment. 5. Patients who have received strong or moderate CYP3A4 inhibitors or inducers such as ketoconazole, erythromycin, netupitant, isavuconazole etc. within 5 half-lives or 7 days (whichever is the shortest) prior to the initiation of study treatment. 6. Viral infection with HIV or viral hepatitis type B or C which require antiviral therapy and/or have positive serology test of hepatitis B surface antigen \[HBsAg (+)\] with HBV DNA ≥ 1000 IU/mL, or hepatitis C virus antibody \[anti-HCV Ab (+)\] with HCV RNA (+). If a patient is HBsAg (+) then HBV DNA needs to be tested. If a patient is anti-HCV Ab (+) then the patient needs to be followed for HCV RNA (-) to be enrolled. 7. Uncontrolled systemic infection /or requiring isolation. 8. Patients with previous history of other malignant diseases within the last 5 years (other than adequately treated non-melanotic skin cancer, in-situ carcinoma of the uterine cervix or myelodysplastic syndromes). 9. Patients with ongoing ≥ Grade 2 (CTCAE v5.0) toxicity (except alopecia and hot flashes) related to previous treatment. 10. Patients with baseline QTc interval \> 450 msec (i.e., CTCAE Grade ≥ 2) at screening (within 28 days prior to 1st dose of PEP07, mean of triplicate readings within approximately 5 minutes). 11. Patients with cardiovascular disability status of New York Heart Association (NYHA) ≥ Class III, left ventricular ejection fraction \< 45 % at baseline, history of cardiac ischemia within the past 6 months, or prior history of cardiac arrhythmia requiring treatment. 12. Patients who have undergone any major surgery within 3 weeks prior to first study drug administration after enrollment. 13. Patients with known active central nervous system (CNS) or leptomeningeal involvement. 14. Patients who have had any of the following within 6 months prior to first administration of PEP07 after enrollment: myocardial infarction, severe/unstable angina pectoris, coronary/peripheral artery bypass graft, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, or seizure disorder. 15. Have a history of hypersensitivity reactions or allergic reactions to PEP07 excipients and components. 16. Patients with other medical or psychiatric condition that, in the opinion of the investigator, might interfere with the patient's participation in the trial or interfere with the interpretation of trial results. 17. Others who are ineligible to participate in this clinical study as determined by the PI or designee.