Combination Study With Soluble LAG-3 Fusion Protein Eftilagimod Alpha (IMP321) and Pembrolizumab in Patients With Previously Untreated Unresectable or Metastatic NSCLC, or Recurrent PD-X Refractory NSCLC or With Recurrent or Metastatic HNSCC

Main Inclusion Criteria:

1. Part A (1st line, PD-X naïve NSCLC): histologically- or cytologically-confirmed diagnosis of non-small cell lung carcinoma stage IIIB not amenable to curative treatment or stage IV not amenable to EGFR/ALK based therapy, treatment naïve for systemic therapy given for advanced/metastatic disease (previous palliative radiotherapy for advanced/metastatic disease acceptable)

   Part B (2nd line, PD-X refractory NSCLC): histologically- or cytologically-confirmed diagnosis of NSCLC after failure of first-line treatment (for metastatic disease) with at least 2 cycles of any PD-1/PD-L1 containing based therapy (e.g. nivolumab, pembrolizumab, avelumab, durvalumab, etc.) alone, or in combination with any other immunotherapeutic or chemotherapy given as part of first-line treatment.

   Part C (2nd line PD-X naive HNSCC): Histologically- or cytologically-confirmed recurrent disease not amenable to curative treatment with local or systemic therapy, or metastatic (disseminated) HNSCC of the oral cavity, oropharynx, hypopharynx, and larynx that is considered incurable by local therapies after failure of prior platinum-based therapy.
2. Submission of formalin-fixed diagnostic tumor tissue
3. ECOG performance status 0-1.
4. Expected survival \> 3 months.

Main Exclusion Criteria:

1. For part A (1st line, PD-X naïve NSCLC):

   * The NSCLC can be treated with curative intent with either surgical resection and/or chemoradiation and/or radiation.
   * Has received systemic therapy for the treatment of their stage IV NSCLC. Completion of treatment with chemotherapy and/or radiation as part of neoadjuvant/adjuvant therapy is allowed as long as therapy was completed at least 6 months prior to the diagnosis of metastatic disease.
   * EGFR-sensitizing mutation and/or is EML4 gene/ ALK gene fusion positive (ALK translocation).
   * Lung radiation therapy that is \>30Gy within 6 months of the first dose of trial treatment.

   For Part B (2nd line, PD-X refractory NSCLC):
   * Symptomatic ascites or pleural effusion.
   * \> 1 line of chemotherapy for metastatic disease.
   * Lung radiation therapy that is \>30Gy within 6 months of the first dose of trial treatment.

   For Part C (2nd line PD-X naive HNSCC):
   * Disease is suitable for local therapy administered with curative intent.
   * Previously treated with \> 1 systemic regimens for recurrent and/or metastatic disease.
2. Prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways) (Part A and C only)
3. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137) and was discontinued from that treatment due to a Grade 3 or higher irAE (Part B only)
4. Has received prior chemotherapy, anti-cancer monoclonal antibody, major surgery, another systemic cancer therapy or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to cycle 1 day 1.

   Note: Patients must have recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Patients with ≤Grade 2 neuropathy, alopecia and elevated transaminases in case of liver metastases may be eligible. If patient received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent.
5. Known active central nervous system metastasis and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are radiologically stable: i.e. without evidence of progression documented by repeat imaging performed after therapy completed for CNS metastasis and with at least 4 weeks difference, clinically stable and without requirement for steroid treatment for at least 14 days prior to cycle 1 day 1.
6. Receives continuous systemic treatment with either corticosteroids (\>10 mg daily prednisone equivalents) or other immunosuppressive medications within 7 days prior to cycle 1 day 1. Inhaled or topical steroids and physiological replacement doses of up to 10 mg daily prednisone equivalents are permitted in the absence of active auto-immune disease.