Study to Test the Safety and How Radium-223 Dichloride an Alpha Particle-emitting Radioactive Agent Works in Combination With Pembrolizumab an Immune Checkpoint Inhibitor in Patients With Stage IV Non-small Cell Lung Cancer With Bone Metastases

Inclusion Criteria:

* Histologically or cytologically confirmed diagnosis of stage IV NSCLC.

  * Phase 2 Cohort 1: No Epidermal Growth Factor Receptor (EGFR) / v-Raf murine sarcoma viral oncogene homolog B (BRAF) mutation or anaplastic lymphoma kinase (ALK)/ROS1 rearrangement. Treatment naïve (no prior systemic therapy) for their metastatic NSCLC.
  * Phase 2 Cohort 2: progression on prior treatment with an immune checkpoint inhibitor inhibitor. Prior treatment with platinum-based chemotherapy in combination or in sequence in line with local standard of care.
  * Phase 1 includes participants meeting either Cohort 1 or Cohort 2 criteria.
* Measurable disease per RECIST v1.1.
* At least 2 skeletal metastases.
* Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) of 0 or 1.
* Adequate bone marrow and organ function.
* Participants must be on a bone health agent (BHA) treatment, such as bisphosphonates or denosumab treatment unless such treatment is contraindicated or not recommended per investigator's judgement.

Exclusion Criteria:

* Previous or concurrent cancer within 3 years prior to enrollment.
* 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. Phase 2 Cohort 2: was discontinued from that treatment due to a Grade 3 or higher immune-related AEs (irAEs).
* Known active central nervous system metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, clinically stable, and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment.
* Active autoimmune disease that has required systemic treatment in the past 2 years.
* History of (non-infectious) pneumonitis that required steroids or has current pneumonitis.
* Known history or presence of osteonecrosis of jaw.
* Ongoing infection \>Grade 2 NCI-CTCAE v.5.0 requiring systemic therapy.
* Significant acute GI disorders with diarrhea as a major symptom e.g., Crohn's disease, malabsorption, or ≥ NCI-CTCAE v.5.0 Grade 2 diarrhea of any etiology.
* History of osteoporotic fracture.
* Prior treatment with radium-223 dichloride or any therapeutic radiopharmaceutical.
* Prior radiotherapy within 21 days of planned start of study treatment.