A phase 1, multicenter, open label, non-randomized dose escalation and dose expansion study to examine the maximum tolerated dose, (MTD), minimum effective dose (MED) and/or recommended dose for expansion (RDE) of intratumoral ONM-501 as monotherapy and in combination with a PD-1 checkpoint inhibitor in patients with advanced solid tumors and lymphomas.

This Phase 1, multi-center trial will consist of three parts: monotherapy dose escalation; combination therapy dose finding; and combination therapy dose expansion exploring two doses in specific tumor indication(s). Each dosing cycle of ONM-501 will be 21 days. ONM 501 will be administered as intratumoral injections once per week for three weeks (on Days 1, 8, and 15), followed by three weeks without ONM-501 administration. The monotherapy dose escalation will utilize an accelerated titration method.

The combination agent will be administered according to standard protocol, once every three weeks. This phase will evaluate ONM-501 in combination with approved immune checkpoint inhibitor (ICI) cemiplimab. Enrollment in this phase will follow a "Rolling 6" or 6+0 methodology - up to 6 patients will be enrolled in a staggered format; dose escalation of ONM-501 will be permitted.

Once the recommended doses for expansion (RDEs) are determined for ONM-501 + ICI combination or ONM-501 monotherapy, the expansion phase of this study will be initiated. The expansion phase will enroll patients in one to three indication-specific expansion cohorts.

Inclusion Criteria:

1. Ability to understand and willingness to sign written informed consent before performance of any study procedures
2. Age ≥ 18 years
3. Participants with solid tumors or lymphomas, confirmed by available histopathology records or current biopsy, that are advanced, nonresectable, or recurrent and progressing since last antitumor therapy, and for which no alternative standard therapy exists.
4. Participants must have a minimum of one injectable and measurable lesion.
5. Participants with prior Hepatitis B or C are eligible if they have adequate liver function
6. Participants with human immunodeficiency virus (HIV) are eligible if on established HAART for a minimum of 4 weeks prior to enrollment, have an HIV viral load <400 copies/mL, and have CD4+ T-cell (CD4+) counts ≥ 350 cells/uL
7. Adequate bone marrow function:
8. Adequate liver function

Exclusion Criteria: Patients will be excluded from this study if they meet any of the following criteria (Part 1a and Part 1b).

1. Other malignancy active within the previous 2 years except for basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the cervix or breast that has completed curative therapy.
2. Major surgery within 4 weeks before the first dose of study drug.
3. Brain metastases that are untreated or in the posterior fossa or involve the meninges. Participants with stable or previously treated progressing brain metastases (except in the posterior fossa or involving the meninges) may be permitted in a case-by-case basis at the Sponsor's discretion.
4. Prolongation of corrected QT (QTc) interval to >470 millisecond (ms) for males and females when electrolytes balance is normal.
5. Females who are breastfeeding or pregnant at screening or baseline
6. Females of childbearing potential that refuse to use a highly effective method of contraception.
7. Has uncontrolled or poorly controlled hypertension as defined by a sustained BP > 9. Has received prior investigational therapy within 5 half-lives of the agent or 4 weeks before the first administration of study drug, whichever is shorter.
8. Has had any major cardiovascular event within 6 months prior to study drug 10. Has known hypersensitivity to any component in the formulation of ONM-501
9. Has an active infection requiring systemic treatment
10. Is participating in another therapeutic clinical trial

Additional Exclusion Criteria for ONM-501 in Combination with cemiplimab (Part 1b)

1. Has known hypersensitivity to any component in the formulation of cemiplimab
2. Has any active or recent history of a known or suspected autoimmune disease or recent history of a syndrome that required systemic corticosteroids (>10 mg daily prednisone equivalent)
3. Has a condition requiring systemic treatment with corticosteroids