Inclusion Criteria:

A subject will be eligible for study participation if the subject meets the following criteria:

* Eligible subject must have an advanced hematologic malignancy including:

* MDS with refractory anemia with excess blasts (RAEB; subtype RAEB-1 or RAEB-2) as defined by World Health Organization (WHO) 2016 revised criteria and/or MDS with high- or very high-risk (risk score \> 4.5) per the Revised International Prognostic Scoring System (IPSS-R) (Greenberg et al. 2012) that is relapsed or refractory to prior therapy for MDS, or the subject is intolerant to established therapy known to provide clinical benefit for their condition in the opinion of the Investigator; Or relapsed and/or refractory MDS subjects in whom the Investigators feel would benefit from Arm 2.
* Relapsed and/or primary refractory AML as defined by WHO 2016 revised criteria; Or frontline older and/or unfit AML subjects in whom the Investigators feel would benefit from Arm 2.
* CMML (with ≥ 5% blasts in bone marrow) as defined by WHO 2016 revised criteria that is relapsed and/or refractory and that, in the opinion of the Investigator, requires treatment or that has exhausted treatment options that would be considered standard of care.
* Subject's prior therapies may include other BCL2 inhibitors and other HMA agents for Arm 2.
* Blast count ≤ 30 × 10\^9 cells/L at the time of initiating investigational therapy (hydroxyurea is allowed to control blast count prior to and during therapy).
* Subject must have adequate coagulation, renal, and hepatic function.

* Activated partial thromboplastin time and prothrombin time not to exceed 1.5 × the upper limit of normal (ULN);
* Calculated creatinine clearance (Cr Cl) ≥ 30 mL/min using 24-hour CrCl OR Cockcroft-Gault formula (using actual body weight)
* UK and EU only: Estimated glomerular filtration rate (GFR) ≥ 30 mL/min/1.73m2 using the modification of diet in renal disease (MDRD) equation.
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.0 ×ULN; bilirubin ≤ 1.5 × ULN (except subjects with Gilbert's Syndrome, who may have a bilirubin \> 1.5 × ULN, per discussion between the Investigator and the Medical Monitor).
* Adequate cardiac function defined as: shortening fraction of ≥ 27% by echocardiogram, or ejection fraction of ≥ 50% by 2D echocardiogram without Doppler.

Exclusion Criteria:

A subject will not be eligible for study participation if he/she meets any of the following criteria.

* Subjects with a diagnosis of promyelocytic leukemia/retinoic acid receptor alpha (PML-RARA) or non-PML-RARA rearranged acute promyelocytic leukemia (APL).
* Subjects who have undergone hematopoietic stem cell transplantation (HSCT) within 60 days of the first dose of LP-108, or subjects on immunosuppressive therapy post-HSCT at the time of Screening, or with clinically significant graft-versus-host disease (GVHD). (Subjects in relapse after allogeneic transplantation must be off calcineurin inhibitors for at least 4 weeks. The use of topical steroids and/or up to 20 mg/day prednisone or equivalent systemic steroids for ongoing GVHD is permitted).
* Subject has received any of the following therapies within 14 days or 5 half-lives (whichever is shorter) prior to the first dose of study drug, or has not recovered to ≤ Grade 1 clinically significant adverse effect(s) of the previous therapy:

* Any anti-cancer therapy including chemotherapy, hormonal therapy, biologic or immunotherapy, targeted small molecule agents, etc. (corticosteroid therapy \< 20 mg/day prednisone equivalent for \< 14 days at time of study treatment and hydroxyurea cytoreduction therapy according to institutional guidelines to treat disease associated symptoms are permitted).
* Any investigational therapy.
* There is 28-day washout period required for subject who have had prior CAR-T treatment if there is no evidence of cytokine release syndrome (CRS) or other adverse events related to the CAR-T treatment per discussion with the Medical Monitor.
* Subject has received the following medications or therapies within 7 days or 5 half-lives (whichever is shorter) prior to the first dose of study drug:

* Cytochrome P450, family 3, subfamily A (CYP3A4) strong inhibitors (see Appendix 10 for strong CYP3A4 inhibitors). In Phase 1b of this trial, the criterion regarding CYP3A4 strong inhibitors will be removed at time of amendment of the trial when Phase 1b is to be initiated. The amendment will include recommendations on concomitant dosing of LP-108 and strong CYP3A4 inhibitors such as azole antifungal agents, PK monitoring for the initial weeks on study, as well as closer safety monitoring for subjects.
* Strong CYP3A4 inducers such as rifampin, carbamazepine, phenytoin, and St. John's wort.
* Inhibitors of P-glycoprotein (P-gp) and breast cancer resistance protein (BCRP) (see Appendix 11 for P gp and BCRP inhibitors).
* Immunosuppressive drugs (equivalent to \>10mg prednisone) for underlying autoimmune or rheumatologic conditions.
* All statins as they could inhibit bilirubin uptake transporter OATP1B1 and OATP1B3 (the washout period should always be 5 half-lives) (see Appendix 11)
* Subject has baseline prolongation of the corrected QTc \> 480 ms (calculated per Fridericia's formula \[QTc = QT/RR (1/3)\].
* Subject has a history of other malignancies other than the eligible hematologic malignancy within the past 1 year prior to study entry, with the exception of:

* Subject with breast cancer or prostrate cancer on endocrine therapy with stable disease.
* Adequately treated in situ carcinoma of the cervix uteri;
* Basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin;
* Previous malignancy confined and surgically resected (or treated with other
* Subject exhibits evidence of other clinically significant uncontrolled condition(s) including, but not limited to:

* Uncontrolled systemic infection (bacterial, fungal, viral)
* Known active or poorly controlled human immunodeficiency virus or active hepatitis B or C infection
* Unexplained fever \> 38.5 °C during the Screening period or on their first day of study drug administration (at the discretion of the Investigator, if the fever is considered related to the subject's malignancy may be enrolled).
* Subjects with known and active central nervous system (CNS) involvement (radiographic or cytologic) at Screening; subjects with history of CNS involvement who have no symptoms suggestive of CNS disease and have had at least 2 successful lumbar punctures without cytologic evidence of leukemia may be included after discussion and approval of the Medical Monitor. (Evaluation of cerebrospinal fluid is only required if there is a clinical suspicion of CNS involvement by leukemia during screening in subjects without a history of CNS involvement).
* Subjects with immediate life-threatening, severe complications of leukemia such as uncontrolled bleeding, pneumonia with hypoxia or shock, and/or disseminated intravascular coagulation.
* Requires ongoing treatment with

* Systemic acid-reducing agents including H-2-receptor antagonists and proton pump inhibitors
* Sensitive CYP2C8 substrates (such as montelukast, pioglitazone, repaglinide, rosiglitazone) or CYP2C8 substrates with a narrow therapeutic index (e.g., amiodarone, fosphenytoin, paclitaxel, penprocoumon, phenytoin)