(1) Background: Mutations in epidermal growth factor receptor (EGFR) proteins account for many non-small cell lung cancers (NSCLCs), and EGFR tyrosine kinase inhibitors (TKIs) are being used as targeted therapeutics. However, resistance to TKIs continues to increase owing to additional mutations in more than half of the patients receiving EGFR TKI therapy. In addition to targeting new mutations with next-generation therapeutics, it is necessary to find an alternative target to overcome the challenges associated with resistance. (2) Methods: To identify potential alternative targets in patients with NSCLC undergoing targeted therapy, putative targets were identified by transcriptome profiling and validated for their biological and therapeutic effects in vitro and in vivo. (3) Results: ELF3 was found to be differentially expressed in NSCLC, and ELF3 knockdown significantly increased cell death in K-Ras mutant as well as in EGFR L858R/T790M mutation harboring lung cancer cells. We also found that auranofin, an inhibitor of protein kinase C iota (PKCί), a protein upstream of ELF3, effectively induced cell death. (4) Conclusions: Our study suggests that blocking ELF3 is an effective way to induce cell death in NSCLC with K-Ras and EGFR T790M/L858R mutations and thus advocates the use of auranofin as an effective alternative drug to overcome EGFR TKI resistance.