Enhanced Dermatological Care to Reduce Rash and Paronychia in Epidermal Growth Factor Receptor (EGRF)-Mutated Non-Small Cell Lung Cancer (NSCLC) Treated First-line With Amivantamab Plus Lazertinib

Inclusion Criteria: * Have histologically or cytologically confirmed, locally advanced or metastatic non-small cell lung cancer (NSCLC); Is treatment naive and not amenable to curative therapy including surgical resection or (chemo) radiation. Adjuvant or neoadjuvant therapy for Stage I, Stage II or Stage IIIA disease is allowed if last dose administered more than 12 months prior to the development of locally advanced or metastatic disease * Have a tumor that harbors an epidermal growth factor receptor (EGFR) Exon 19del or Exon 21 L858R substitution, as detected by an Food and Drug Administration (FDA)-approved or other validated test in a clinical laboratory improvement amendments (CLIA)-certified laboratory (sites in the United States) or an accredited local laboratory (sites outside of the United States) in accordance with site standard-of-care * A participant with asymptomatic or previously treated and stable brain metastases may participate in this study. Participants with a history of symptomatic brain metastases must have had all lesions treated as clinically indicated (that is, no current indication for further definitive local therapy). Any definitive local therapy to brain metastases must have been completed at least 14 days prior to randomization, and the participant can be receiving no greater than 10 milligram (mg) prednisone or equivalent daily for the treatment of intracranial disease * Can have prior or concurrent second malignancy (other than the disease under study) which natural history or treatment is unlikely to interfere with any study endpoints, safety, or the efficacy of the study treatment(s). For the amivantamab SC expansion cohorts: Due to the increased risk of skin cancer with ruxolitinib, participants with any prior or concurrent skin malignancies will be excluded * Sub-study: Participants must have new-onset or persistent (defined as non-responsive to standard of care \[SoC\]) Grade \>=2 specific DAEIs of the scalp, face, or body, as defined by NCI-CTCAE Grading v5.0 for DAEIs (excluding paronychia) Exclusion Criteria: * History of uncontrolled illness, including but not limited to uncontrolled diabetes; ongoing or active infection (includes infection requiring treatment with antimicrobial therapy \[participants will be required to complete antibiotics 1 week prior to starting background anticancer treatment\] or diagnosed or suspected viral infection). For the amivantamab SC expansion cohorts, this includes active localized serious infections; active bleeding diathesis; impaired oxygenation requiring continuous oxygen supplementation; refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product, or previous significant bowel resection that would preclude adequate absorption of background anticancer treatment or doxycycline/minocycline; psychiatric illness, social situation, or any other circumstances that would limit compliance with study requirements; any ophthalmologic condition that is clinically unstable; pre-existing skin condition that would prevent adequate evaluations of dermatologic toxicity, as determined by the investigator * Medical history of interstitial lung disease (ILD), including drug-induced ILD or radiation pneumonitis * Known allergy, hypersensitivity, or intolerance to the excipients of amivantamab, lazertinib, or to tetracyclines, doxycycline, minocycline, timolol\*, ruxolitinib\*, zinc\*, corticosteroids\* or their excipients or to any component of the enhanced dermatologic management (\*for the amivantamab SC expansion cohorts) * Participant has received any prior systemic treatment at any time for locally advanced stage III B/C or metastatic stage IV disease (adjuvant or neoadjuvant therapy for stage I, II or IIIA disease is allowed if last dose administered more than 12 months prior to the development of locally advanced or metastatic disease) * Participant has an active or past medical history of leptomeningeal disease * Sub-study: Participants who have received prior treatment for epidermal growth factor receptor (EGFR)-induced DAEIs with JAK inhibitors (for Cohort A) or calcineurin inhibitors (for Cohort B)