This study focuses on people with non-small cell lung cancer (NSCLC) who have a specific mutation in a gene called the epidermal growth factor receptor (EFGR) gene. The purpose of the study is to learn more about the effectiveness and safety of the combination of a drug called amivantamab (given under the skin) and chemotherapy, as well as the effectiveness and safety of the combination of amivantamab (given under the skin) and another drug, lazertinib. Patients will be asked to participate in 1 of 2 groups, based on their prior treatment history for NSCLC. In Group 1, participants will receive amivantamab injection (under the skin) and lazertinib (daily by mouth). In Group 2, participants will receive amivantamab injection and chemotherapy (carboplatin and pemetrexed). Study procedures for both groups include physical exams, blood and urine sample collection, imaging scans, and tumor biopsy. Amivantamab is an antibody, which is a protein that specifically recognizes and binds to other types of proteins called antigens. Antibodies and antigens can work together to help the immune system fight cancer cells. Lazertinib belongs to a class of drugs called EGFR tyrosine kinase inhibitors. When a tyrosine kinase inhibitor binds to EGFR on a cancer cell, the growth of the cell is slowed down or stopped. While amivantamab and lazertinib are approved by the U.S. Food and Drug Administration (FDA), the use of amivantamab given as an injection under the skin in this study is investigational.