This Study Tests How BI 754111 is Distributed in Patients With Advanced Non-small Cell Lung Cancer or Patients With Head and Neck Cancer Who Are Treated With BI 754091

Inclusion Criteria:

* Provision of signed and dated, written Informed Consent Form (ICF) prior to any trial specific procedures, sampling, or analyses
* Patients of legal age (according to local legislation) at the time of signature of the ICF
* Patients with histologically confirmed diagnosis of recurrent NSCLC who received anti- PD-1 or anti PD-L1 as Part of last treatment with at least 3 months of stable disease (i.e.patients with confirmed response (PR or CR) regardless of duration of response or stable disease (SD) for a minimum of 3 months) and have become refractory to anti-PD- 1/ anti-PD-L1 based treatment OR

  --Patients with histologically confirmed diagnosis of recurrent metastatic HNSCC who progressed after platinum based therapy or not indicated for receiving standard (radio) chemotherapy (previous treatment with anti- PD-1/ PD-L1 is allowed)
* Eastern Cooperative Oncology Group (ECOG, R01-0787) score: 0 to 1
* Patient must have at least one PET imageable and evaluable tumor lesion of 20mm
* Patients must have at least one tumor lesion amenable to biopsy. This lesion should be PET imageable and evaluable as defined above and the biopsy should be obtained before first BI 754091 administration, unless medically contra-indicated. In the latter case, 25 4μm sections from an archival biopsy taken at relapse after the previous treatment are acceptable
* Must have evaluable lesion(s) according to Revised Response Evaluation Criteria in Solid Tumors (RECIST) Version 1.1 and iRECIST
* Life expectancy of at least 12 weeks after the start of the treatment according to the Investigator's judgement
* Male or female patients. Women of childbearing potential (WOCBP)1 and men able to father a child must be ready and able to use highly effective methods of birth control per International Conference on Harmonisation (ICH) M3 (R2) (that result in a low failure rate of less than 1% per year when used consistently and correctly) during trial Participation and for at least 6 months after the last administration of trial medication. A list of contraception methods meeting these criteria is provided in the patient information.

Exclusion Criteria:

* Not having fully recovered from major surgery before they enter into the trial according to investigator judgment or planned for major surgery within 12 months after screening, e.g. hip replacement
* Patients who must or wish to continue the intake of restricted medications or any drug considered likely to interfere with the safe conduct of the trial
* Patients not expected to comply with the protocol requirements or not expected to complete the trial as scheduled
* Previous treatment in this trial
* Any investigational or anti-tumor treatment within 4 weeks or within 5 half-life periods (whichever is shorter) prior to the initiation of trial treatment.
* Any unresolved toxicities from prior therapy greater than CTCAE Grade 1 at the time of starting study treatment with the exception of alopecia and Grade 2 neuropathy due to prior platinum-based therapy
* Prior treatment with anti-LAG-3 agents
* Presence of other active invasive cancers other than the one treated in this trial, with the exception of resected/ablated basal or squamous-cell carcinoma of the skin or carcinoma in situ of the cervix, or other local tumors considered cured by local treatment
* Untreated brain metastasis(es) that may be considered active. Patients with previously treated brain metastases may Participate provided they are stable (i.e., without evidence of PD by imaging for at least 4 weeks prior to the first dose of trial treatment, and any neurologic symptoms have returned to baseline), and there is no evidence of new or enlarging brain metastases
* Inadequate organ function or bone marrow reserve as demonstrated by the laboratory values
* Any of the following cardiac criteria:

  * Mean resting corrected QT interval (QTc) \>470 msec
  * Any clinically important abnormalities in rhythm, conduction, or morphology of resting ECGs, e.g., complete left bundle branch block, third degree heart block
  * Any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as heart failure, hypokalaemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years-of-age, or any concomitant medication known to prolong the QT interval
  * Ejection fraction \<55% or the lower limit of normal of the institutional standard.
* History of pneumonitis within the last 5 years
* History of severe hypersensitivity reactions to other mAbs
* Immunosuppressive corticosteroid doses (\>10 mg prednisone daily or equivalent) within 4 weeks prior to the first dose of study treatment.
* Active autoimmune disease or a documented history of autoimmune disease, except vitiligo or resolved childhood asthma/atopy
* Active infection requiring systemic treatment (antibacterial, antiviral, or antifungal therapy) at start of treatment in this trial
* Known history of human immunodeficiency virus infection or an active hepatitis B or C virus infection
* Interstitial lung disease
* Chronic alcohol or drug abuse or any condition that, in the investigator's opinion, makes him/her an unreliable trial patient or unlikely to complete the trial or unable to comply with the protocol procedures
* Women who are pregnant, nursing, or who plan to become pregnant in the trial