Study of MK-2118 Administered as Intratumoral Injection as Monotherapy and in Combination With Pembrolizumab (MK-3475) or by Subcutaneous Injection in Combination With Pembrolizumab in the Treatment of Adults With Advanced/Metastatic Solid Tumors or Lymphomas (MK-2118-001)

Inclusion Criteria:

Arms 1 and 2 Participants:

* Has any histologically or cytologically confirmed advanced/metastatic solid tumor by pathology report and has received, or have been intolerant to all treatment known to confer clinical benefit. Solid tumors and lymphomas of any type are eligible for enrollment. For cutaneous T-cell lymphoma (CTCL), histopathological diagnosis should be confirmed in a skin biopsy representative of disease.
* Has Stage III or Stage IV disease that is not surgically resectable. Stage IIB (T3N0M0B0-1) CTCL participants are eligible.

Arm 3 Participants:

\- Has metastatic liver and/or liver lesion involvement that does not exceed one third of the total liver volume in participants to be treated by liver IT injection. Hepatocellular carcinoma participants are excluded from eligibility of IT liver injection.

All Participants:

* Has Stage III or Stage IV disease that is not surgically resectable.
* Has ≥1 injectable lesion that is amenable to injection and biopsy via visual inspection for a cutaneous lesion, or via ultrasound guidance for a subcutaneous lesion.
* Has ≥1 discrete, distant noninjected lesion that is amenable to biopsy via visual inspection or amenable to biopsy via image guidance.
* Has Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1.
* Demonstrates adequate organ function.
* A male participant is eligible to participate if he agrees to the following during the intervention period and for at least 120 days after the last dose of study intervetnion:

  1. Refrain from donating sperm.
  2. Be abstinent from heterosexual intercourse as their preferred and usual lifestyle and agree to remain abstinent OR must agree to use contraception unless confirmed to be azoospermic.
* A female participant is eligible to participate if she is not pregnant or breastfeeding, and at least one of the following conditions applies:

  1. Is not a woman of childbearing potential (WOCBP).
  2. Is a WOCBP and using a contraceptive method that is highly effective with low user dependency, or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis), during the intervention period and for at least 120 days after the last dose of study intervention, AND agrees not to donate eggs (ova, oocytes) to others or freeze/store for her own use for the purpose of reproduction during this period.
* Human Immunodeficiency Virus (HIV)-infected participants must meet these additional criteria:

  1. Has HIV-1 infection documented by laboratory test.
  2. Has well-controlled HIV on antiretroviral therapy (ART), defined as: 1) must have a CD4+ T-cell count \>350 cells/mm\^3 at time of screening; 2) must have achieved and maintained virologic suppression defined as confirmed HIV ribonucleic acid (RNA) level \<50 or below the lower limit of quantification (LLOQ) using the locally available assay at the time of screening and for ≥12 weeks prior to screening; and 3) must have been on a stable regimen, without changes in drugs or dose modification, for ≥4 weeks prior to study entry (Day 1).

Exclusion Criteria:

* Has history of a second malignancy, unless potentially curative treatment has been completed, with no evidence of malignancy for 2 years (except for successful definitive resection of basal cell carcinoma of the skin, superficial bladder cancer, or in situ cervical cancer).
* Has clinically active central nervous system metastases and/or carcinomatous meningitis.
* Has severe hypersensitivity reaction to treatment with a monoclonal antibody (mAb).
* Has active autoimmune disease that has required systemic treatment in the past 2 years.
* Has history of vasculitis.
* Has active infection requiring therapy.
* Has history of (noninfectious) pneumonitis that required steroids or current pneumonitis.
* Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years.
* Has known Hepatitis B or C infection.
* Has known psychiatric or substance abuse disorders that would interfere in cooperation with the requirements of the trial.
* Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study.
* Is not fully recovered from any effects of major surgery, and is free of significant detectable infection.
* HIV-infected participants with history of Kaposi's sarcoma and/or multicentric Castleman's disease.
* HIV-infected participants who have had an HIV-related opportunistic infection within 6 months.
* Has had chemotherapy, definitive radiation, or biological cancer therapy within 4 weeks (2 weeks for palliative radiation) prior to the first dose of study treatment, or has not recovered to baseline or Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 from the AEs due to cancer therapeutics administered \>4 weeks earlier.
* Has been treated within 2 weeks of Cycle 1 Day1 with any of the following: strong/moderate Cytochrome P450 2C9 (CYP2C9) inhibitors, such as: amiodarone, felbamate, fluconazole, miconazole, piperine, oxandrolone, fluorouracil and its derivatives (combination drug tegafur/gimeracil/oteracil \[TS-1\], Uftoral \[UFT\], tegafur, carmofur, doxifluridine, capecitabine), sulfaphenazole, cyclosporine, bucurol, tienilic acid; UGT1A3 inhibitors (including ritonavir, quinidine, probenecid, and valproic acid); or strong carbonyl reductase (CBR) inhibitors (including quercetin, menadione, glycyrrhetinic acid, and flufenamic acid).
* Is currently participating and receiving study therapy or has participated in a study of an investigational agent and has received study therapy or has used an investigational device within 28 days of administration of MK-2118.
* Is expected to require any other form of antineoplastic therapy while on study.
* Is on chronic systemic steroid therapy in excess of replacement doses (prednisone ≤10 mg/day is acceptable), or on any other form of immunosuppressive medication. For CTCL, continued use of either prednisone ≤10 mg/day or continued use of topical steroids is acceptable.
* Has received a live vaccine within 28 days prior to first dose.
* Has been treated with a stimulator of interferon genes (STING) agonist (eg, MK-1454, ADU-S100 \[synthetic cyclic dinucleotide (CDN)\]).
* Has a history of re-irradiation for head and neck squamous cell carcinoma (HNSCC) at the projected injection site.
* Has a tumor(s) in direct contact or encases a major blood vessel and has ulceration and/or fungation onto the skin surface at the projected injection site.