Effects of Single Agent Niraparib and Niraparib Plus Programmed Cell Death-1 (PD-1) Inhibitors in Non-Small Cell Lung Cancer Participants

General Inclusion Criteria: * Male or female participants at least 18 years of age. * Histological or cytological proven advanced (unresectable) or metastatic NSCLC as defined as stage IIIB (positive supraclavicular lymph nodes) not amenable to definitive chemoradiotherapy or stage IV NSCLC. * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. * Adequate organ function, defined as: 1. Absolute neutrophil count (ANC) \>= 1500 per microliter (/µL). 2. Platelets \>= 100,000/µL. 3. Hemoglobin \>= 9 grams per deciliter (g/dL) or \>= 5.6 millimoles per liter (mmol/L). 4. Serum creatinine \<= 1.5 times upper limit of normal (ULN) or creatinine clearance \>= 50 milliliters per minute (mL/min) (as calculated using the Cockcroft Gault equation or measured using 24-hour urine creatinine clearance) for participants with creatinine levels \> 1.5 times institutional ULN. 5. Total bilirubin \<= 1.5 times ULN except in participants with Gilbert's syndrome. Participants with Gilbert's syndrome may enroll if direct bilirubin \<= 1.5 times ULN of the direct bilirubin. 6. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \<= 2.5 times ULN unless liver metastases are present, in which case they must be \<= 5 times ULN. * Participant must have recovered to Grade 1 toxicity from prior cancer therapy (a participant with Grade 2 neuropathy or Grade 2 alopecia is an exception to this criterion and may qualify for this study). * Participant agrees to submit formalin fixed paraffin embedded (FFPE) tumor tissue specimen, which may have been collected at any time prior to screening. If no archival FFPE tumor tissue is available, participant agrees to undergo a tumor tissue biopsy before Cycle 1/Day 1. (For Cohort 3 only: if diagnosis was made by cytology and archival tissue is not available, participant will not need to provide tumor tissue). * Participants is able to take oral medications. * Female participant meets the following criteria: a) Female participant (of childbearing potential) is not breastfeeding, has a negative serum pregnancy test within 72 hours prior to taking study drug, and agrees to abstain from activities that could result in pregnancy from enrollment through 180 days after the last dose of study treatment or is of nonchildbearing potential; or b) Female participant is of nonchildbearing potential, other than medical reasons, defined as follows: i) \>=45 years of age and has not had menses for \> 1 year. ii) Amenorrheic for \< 2 years without a hysterectomy and oophorectomy and a follicle-stimulating hormone (FSH) value in the postmenopausal range upon screening evaluation. iii) Post hysterectomy, bilateral oophorectomy, or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure, otherwise the participant must be willing to use 2 highly effective contraception methods throughout the study, starting with the screening visit through 180 days after the last dose of study therapy. * Male participant agrees to use an adequate method of contraception and not donate sperm starting with the first dose of study therapy through 120 days after the last dose of study therapy. * Participant is able to understand the study procedures and agree to participate in the study by providing written informed consent. Cohort Specific Inclusion Criteria: * Cohorts 1 and 1A (combination of niraparib and PD-1 inhibitor): participants must have tumors with high PD-L1 expression (TPS \>= 50%) per local assessment; with no known Epidermal Growth Factor Receptor (EGFR)-sensitizing mutation and/or ROS -1 or anaplastic lymphoma kinase (ALK) translocation, and no prior systemic chemotherapy or PD-1/PD-L1 inhibitor treatment for metastatic NSCLC. * Cohorts 2 and 2A (combination of niraparib and PD-1 inhibitor): participants must have tumors with PD-L1 expression (TPS between 1% and 49%) per local assessment, with no known EGFR-sensitizing mutation and/or ROS-1 or ALK translocation, and no prior systemic chemotherapy or PD-1/PD-L1 inhibitor treatment for metastatic NSCLC. * Cohort 3 (single agent niraparib): participants must have metastatic squamous non-small cell lung cancer (sqNSCLC) and have progressed after both prior platinum-based chemotherapy and prior PD-1 or PD-L1 inhibitor treatment. Exclusion Criteria for Cohorts 1, 1A , 2 and 2A: * Participant has received systemic therapy for the treatment of advanced stage 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. * Prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Known hypersensitivity to the components of niraparib, pembrolizumab, TSR-042 (Dostarlimab), or their excipients. * Known EGFR (exon 19 and 21) mutations, ALK translocations, and/or ROS-1 translocations. * Participant has a history or current condition (such as transfusion-dependent anemia or thrombocytopenia), therapy, or laboratory abnormality that might confound the study results, or interfere with the participant's participation for the full duration of the study treatment. * Known diagnosis of immunodeficiency or receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment. * Participant is immunocompromised, in the opinion of the Investigator. * Current participation in a treatment study or past participation in a study of an investigational agent within 4 weeks before the first dose of study treatment. * Symptomatic uncontrolled brain or leptomeningeal metastases. (To be considered "controlled," central nervous system \[CNS\] disease must have undergone treatment \[example, radiation or chemotherapy\] at least 1 month prior to study entry. The participant must not have any new or progressive signs or symptoms related to the CNS disease and must be taking \<= 10 mg of prednisone or equivalent per day or no steroids.) Participants who have untreated brain metastases and who are not symptomatic may enroll if the Investigator feels that treatment of these metastases is not indicated. A scan to confirm the absence of brain metastases is not required. Participants with spinal cord compression may be considered if they have received definitive treatment for this and evidence of clinically SD for 28 days. * Active autoimmune disease that required systemic treatment in the past 2 years (with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (examples, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment. * Major surgery within 3 weeks of starting the study or participant has not recovered from any effects of any major surgery. * Other active concomitant malignancy that warrants systemic therapy. * Poor medical risk due to a serious, uncontrolled medical disorder, nonmalignant systemic disease, or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 90 days) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, uncontrolled hypertension, active uncontrolled coagulopathy or any psychiatric disorder that prohibits obtaining informed consent. * Known history of interstitial lung disease, drug-related pneumonitis, or radiation pneumonitis requiring steroid treatment. * Participant is pregnant, breastfeeding, or expecting to conceive children while receiving study treatment and for 180 days (for pregnancy or conception) or 30 days (for breastfeeding) after the last dose of study treatment. * Male participant is expecting to donate sperm or father children while receiving study drug or for 120 days after the last dose of study treatment. * Known active hepatic disease (known hepatic cirrhosis, hepatitis B surface antigen-positive status, or suspected active hepatitis C infection). * Prior treatment with a known poly adenosine diphosphate-ribose (ADP-ribose) polymerase (PARP) inhibitor. * Participant received a live vaccine within 30 days of planned start of study therapy. * Known history of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML). Exclusion criteria for Cohort 3: * Platinum-treated participant who progressed while on or within less than 8 weeks from the last day of platinum administration. * Known hypersensitivity to the components of niraparib or excipients. * Participant has a history or current condition (such as transfusion dependent anemia or thrombocytopenia), therapy, or laboratory abnormality that might confound the study results, or interfere with the participant's participation for the full duration of the study treatment. * Known diagnosis of immunodeficiency or receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment. * Current participation in a treatment study or past participation in a study of an investigational agent within 4 weeks before the first dose of study treatment. * Symptomatic uncontrolled brain or leptomeningeal metastases. (To be considered "controlled," CNS disease must have undergone treatment \[example, radiation or chemotherapy\] at least 1 month prior to study entry. The participant must not have any new or progressive signs or symptoms related to the CNS disease and must be taking \<= 10 mg of prednisone or equivalent per day or no steroids.) Participants who have untreated brain metastases and who are not symptomatic may enroll if the investigator feels that treatment of these metastases is not indicated. A scan to confirm the absence of brain metastases is not required. Participants with spinal cord compression may be considered if they have received definitive treatment for this and evidence of clinically SD for 28 days. * Major surgery within 3 weeks of starting the study or participant has not recovered from any effects of any major surgery. * Other active concomitant malignancy that warrants systemic therapy. * Poor medical risk due to a serious, uncontrolled medical disorder, nonmalignant systemic disease, or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 90 days) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, uncontrolled hypertension, active uncontrolled coagulopathy, or any psychiatric disorder that prohibits obtaining informed consent. * Known history of interstitial lung disease, drug-related pneumonitis, or radiation pneumonitis requiring steroid treatment. * Participant is pregnant, breastfeeding, or expecting to conceive children, while receiving study treatment and for 180 days (for pregnancy or conception) or 30 days (for breastfeeding) after the last dose of study treatment. * Male participant is expecting to donate sperm or father children while receiving study drug or for 120 days after the last dose of study treatment. * Participant is immunocompromised, in the opinion of the Investigator. * Known active hepatic disease (known hepatic cirrhosis, hepatitis B surface antigen-positive status, or suspected active hepatitis C infection). * Prior treatment with a known PARP inhibitor. * Known history of MDS or AML.