Additional Study Information: This is a research study evaluating a new investigational drug, called CLN-081. CLN-081 is a type of drug called a tyrosine kinase inhibitor. It targets a mutation in the tumor cell called EGFR exon 20 insertion with the goal to slow down or stop cancer cell growth. It is taken orally (by mouth). There are several different parts to this study, each with different study objectives, eligibility for entry and schedules of treatment. Participants at Columbia University Irving Medical Center may take part in either Module B Part 2 or Module C. If you are enrolled to Module B, part 2, the purpose will be to assess the safety and tolerability of the chosen phase 2 dose of CLN-081. If you are enrolled to Module C, the purpose will be to evaluate the safety, tolerability, and antitumor activity of CLN-081 at a dose of 100mg twice a day without food in participants who have non-small cell lung cancer (NSCLC) harboring epidermal growth factor receptor (EGFR) exon 20 insertion mutations, and whose disease has progressed during or after prior treatment with a medication approved by the US FDA for the treatment of EGFR ex20ins mutant NSCLC.