(1) Background: The endocrine system has become a prominent target to autoimmune damage during treatment with immune checkpoint inhibitors (ICIs) in cancer patients. Real-world data regarding endocrine immune-related adverse events (irAEs) are needed to explore their impact in cancer patients. An analysis was conducted to evaluate endocrine irAEs caused by ICIs, besides the challenges and limitations of daily medical practice in oncology in Romania. (2) Methods: This was a retrospective cohort study of lung cancer patients treated with ICIs at Coltea Clinical Hospital, Bucharest, Romania, from 1 November 2017 to 30 November 2022. Endocrine irAEs were identified through endocrinological assessment and were distinguished as any occurring endocrinopathy during treatment with ICIs and related to immunotherapy. Descriptive analyses were performed. (3) Results: Of 310 cancer patients treated with ICIs, we identified 151 with lung cancer. From this cohort, 109 NSCLC patients qualified for baseline endocrine estimation and 13 patients (11.9%) developed endocrine irAEs, such as hypophysitis (4.5%), thyroid disorder (5.5%) and primary adrenal insufficiency (1.8%), with one or more endocrine glands being affected. There might be a correlation between endocrine irAEs and duration of ICI treatment. (4) Conclusions: Early diagnosis and adequate management of endocrine irAEs may be challenging in lung cancer patients. A high incidence of endocrine irAEs is expected with the growing use of ICIs, and because not all endocrine events are immune-related, cooperation between oncologists and endocrinologists is crucial in the management of these patients. More data are needed to confirm the correlation between endocrine irAEs and the efficacy of ICIs.