Epidermal growth factor receptor-tyrosine kinase inhibitors (EGFR-TKIs) are effective in the treatment of advanced non-small-cell lung cancer (NSCLC) with leptomeningeal metastases (LM); however, a proportion of the patients with resistant tumors do not benefit from EGFR-TKI treatment. In the present study the case of a female patient with advanced lung adenocarcinoma harboring the EGFR L858R mutation (encoded in exon 21) who developed intracranial metastases following treatment with erlotinib after gefitinib failure is reported. The patient achieved a partial response (PR) after four cycles of chemotherapy with pemetrexed/cisplatin. However, after 4 months, LM were detected. The patient was treated with osimertinib, a third-generation EGFR-TKI, but the LM continued to progress and the patient eventually succumbed to the disease (overall survival, 6 months). Therefore, LM in patients without the EGFR T790M mutation (encoded in exon 20) appear to be resistant to treatment with the third-generation TKI osimertinib, which may be associated with human epidermal growth factor receptor 2 amplification. Further clinical trials are required to confirm our results.