Inclusion Criteria:  Each potential subject must fulfil all of the following criteria to be enrolled in the study.  Be at least 18 years of age and < 80 years old. Must sign an informed consent form (ICF) indicating that he or she understands the purpose of and procedures required for the trial and are willing to participate in the trial prior to any other trial-related assessments or procedures. Consent is to be obtained prior to the initiation of any study-related tests or procedures that are not part of standard of care for the subject's disease.  Has histologically or cytologically confirmed relapsed and/or refractory B-cell NHL, CLL/SLL or AML with no available standard therapy or is not a candidate for available standard therapy, and for whom, in the opinion of the investigator, experimental therapy with ETH-155008 may be beneficial.  In addition, the following disease-specific criteria outlined below must be met.  a. For all indolent NHL (FL, MZL and Waldenström Macroglobulinemia), previously treated with at least 2 prior lines of systemic therapy with at least 1 line being an anti-CD20 antibody-containing combination regimen.  b. For aggressive NHL (DLBCL, HGBCL, and PMBCL), received, or not eligible for high-dose chemotherapy containing anti-CD20 monoclonal antibodies and autologous stem cell transplantation with curative intent.  c. For MCL, previously treated with at least 1 prior line of systemic therapy including an anti-CD20 antibody combination regimen, with no other approved therapies that would be more appropriate in the investigator's judgement.  d. For CLL/SLL, relapsed or refractory with at least 2 prior lines of systemic therapy using different treatment regimens including BTK inhibitors or venetoclax.  e. For AML, AML diagnosis according to the 2016 World Health Organization (WHO) classification who have received no more than 3 prior lines of therapy and with no available therapy.  Has one of the following RB POSITIVE B-cell NHL subtypes or AML for the Dose Expansion:  Aggressive NHL (DLCBL, HGBCL and PMBCL) MCL, AML Note: at screening, archived or fresh tumor tissue will be assayed by local sites and may need to be confirmed by a central lab later to evaluate Rb expression. Rb IHC staining intensity will be deemed positive if a staining level of 1+ or greater above background is identified. Presence of measurable or evaluable disease. Eastern Cooperative Oncology Group (ECOG) performance status grade of 0 or 1 (dose escalation cohorts) or ≤2 (dose expansion cohorts) (Appendix 1).  For B-NHL, hematology laboratory parameters must be within the following ranges. Values must be without transfusions or growth factors for at least 7 days prior to the first dose of study drug.  Hemoglobin ≥8 g/dL Platelets ≥75×109 /L Absolute neutrophil count ≥1.0×109 /L If neutropenia or thrombocytopenia is believed to be due to marrow infiltration with malignant cells then the absolute neutrophil 0.75x10 9 /L (750/µL) or platelet count ≥ 50x10 9 /L (50,000/µL). For AML, WBC count, no upper limit at Screening, but must be <10 x109/L on Day 1 prior to the first dose of study drug. Note: Subjects with excessive blasts may be treated with hydroxyurea until 2 days prior to first dose of study drug to reduce WBC; Platelet count >10,000/µL; Platelet transfusion prior to first dose is permitted. INR/PT and aPTT ≤1.5 times institutional upper limit of normal (ULN).  Clinical chemistry laboratory parameters must be within the following range:  Aspartate aminotransferase (AST), alanine aminotransferase (ALT), GGT, and alkaline phosphatase ≤2.5×upper limit of normal (ULN). Serum total bilirubin ≤1.5×the ULN. Creatinine clearance ≥60 mL/min (Cockcroft-Gault formula). Cardiac parameters within the following range: corrected QT interval (QTc intervals corrected using Fridericia's formula [QTcF]) ≤470 milliseconds based on the average of triplicate assessments performed no more than 5 minutes apart (±3 minutes). Life expectancy of at least 3 months. A woman of childbearing potential must have a negative serum beta-human chorionic gonadotropin (beta-hCG) at screening and prior to the first dose of study drug. Women must be (as defined in Appendix 3, Contraceptive Guidance and Pregnancy): a. Not of childbearing potential b. Of childbearing potential and - Practicing a highly effective, preferably user-independent method of contraception (failure rate of <1% per year when used consistently and correctly) and agrees to remain on a highly effective method while receiving study drug and until 90 days after last dose. Examples of highly effective methods of contraception are in Appendix 3, Contraceptive Guidance and Pregnancy. In addition to the user-independent, highly effective method of contraception, a male or female condom is required. Male condoms and female condoms should not be used together (due to risk of failure with friction). A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control, e.g., either condom with or partner with occlusive cap (diaphragm or cervical/vault caps). Men or women must agree not to donate sperm or eggs (ova, oocytes) for the purposes of assisted reproduction during the study and for at least 3 months after the last study drug administration. For Part 2 (dose expansion): for B-cell NHL, tumor tissue availability is required at baseline unless clinically contraindicated. Must be willing and able to adhere to the requirements and restrictions specified in the ICF and this protocol.  Exclusion Criteria:  Any potential subject who meets any of the following criteria will be excluded from participating in the trial.  Primary central nervous system (CNS) lymphoma or known CNS involvement at screening, unless treated and stable for ≥3 months with no need for steroids or anti-epileptic medications. Prior solid-organ transplantation. Prior treatment with allogenic stem cell transplant ≤6 months before the first dose of study drug, has evidence of graft versus host disease, or requires immunosuppressant therapy. Autologous HSCT within 3 months before the first dose of ETH-155008. Active autoimmune disease within the past 2 years requires systemic immunosuppressive medications (ie, chronic corticosteroid, methotrexate, or tacrolimus). Toxicities from previous anti-cancer therapies have not resolved to baseline levels or to Grade 1 or less except for alopecia and peripheral neuropathy.  Has known past or current malignancy other than inclusion diagnosis, except for:  Cervical carcinoma of Stage 1B or less. Non-invasive basal cell or squamous cell skin carcinomas. Non-invasive, superficial bladder cancer. Prostate cancer with a current PSA level < 0.1 ng/mL. malignancy which in the opinion of the investigator, with concurrence with the sponsor's medical monitor, is considered cured with minimal risk of recurrence within 1 year before the first dose of study drug. Any curable cancer with a CR of > 2 years duration. Prior treatment with a CDK4/6 or Pim inhibitor. Known allergies, hypersensitivity, or intolerance to ETH-155008 or its excipients. Prior chemotherapy within 3 weeks prior to first treatment, targeted therapy, immunotherapy, radiotherapy, or treatment with an investigational anticancer agent (including investigational vaccines) within 2 weeks before the first administration of ETH-155008. For investigational agents where half-life is known, there should be a treatment-free window of at least 2 weeks or 5 half-lives.  Corticosteroids >10 mg daily prednisone equivalents:  • A short course (ie, >10 mg daily prednisone equivalents for less than 7 days) of corticosteroids is permitted. Inhaled or topical steroids, and adrenal replacement doses ≤10 mg daily prednisone equivalents, are permitted in the absence of active autoimmune disease.  • If corticosteroids were used to treat immune-related adverse events associated with prior therapy, ≥7 days must have elapsed since the last dose of corticosteroid.  History of clinically significant cardiovascular disease within the 6 months prior to the first dose of study drug including, but not limited to: Myocardial infarction Severe or unstable angina Clinically significant cardiac arrhythmias Uncontrolled (persistent) hypertension: systolic blood pressure >159 mmHg; diastolic blood pressure >99 mmHg Stroke or transient ischemic attack Venous thromboembolic events (i.e., pulmonary embolism) within 1 month prior to the first dose of study drug; uncomplicated (Grade ≤2) deep vein thrombosis is not considered exclusionary. Congestive heart failure (New York Heart Association class III-IV) Pericarditis or clinically significant pericardial effusion Myocarditis Endocarditis 13. Clinically significant pulmonary compromise, particularly the need for supplemental oxygen to maintain adequate oxygenation.  14. Unable to swallow capsules or tablets or malabsorption syndrome, disease significantly affecting GI function, or resection of the stomach or small bowel, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction. If any of these conditions exist, the site should discuss with the sponsor to determine subject eligibility.  15. Evidence of active viral, bacterial, or uncontrolled systemic fungal infection requiring parenteral treatment within 2 weeks before the first dose of study drug.  16. Active or chronic hepatitis B or hepatitis C infection.  • Hepatitis B infection is defined by a positive test for hepatitis B surface antigen (HBsAg), or HBsAg negative and positive for anti-hepatitis B core antigen (HBc) with or without anti-HBs.  • Hepatitis C infection is defined by a positive hepatitis C virus (HCV) ribonucleic acid (RNA).  17. Tested HIV positive at screening. 18. Trauma or major surgery (e.g., requiring general anesthesia) within 28 days prior to the first dose of study drug. Note: Subjects with planned surgical procedures to be conducted under local anesthesia may participate.  19. Any serious underlying medical or psychiatric condition (e.g., alcohol or drug abuse), dementia or altered mental status; or any issue that would impair the ability of the subject to receive or tolerate the planned treatment at the investigational site, to understand informed consent, or that in the opinion of the investigator would contraindicate the participation in the study or confound the protocol-specified assessments or results of the study.  20. Requires a prohibited medication that cannot be discontinued or substituted, or temporally interrupted during the study; see Section 6.6.2 for prohibited therapies.  21. Are currently taking or have previously taken a sensitive oral CYP3A4 substrate or an oral 3A4 substrate with narrow therapeutic window (an at least 5 x half-life washout will be required).  22. Are currently taking or have taken a potent CYP3A4 or p-glycoprotein inducer or inhibitors (inclusive of prescription and over-the-counter medication and/or herbal products). An at least 2-week (or at least 5 x half-life washout for long half-life products) will be required.