This study is open to adults 18 years and older with advanced or metastatic non-small cell lung cancer. People can join the study if they have tumours with HER2 mutations and have not yet received any systemic therapy including chemotherapy for advanced or metastatic lung cancer. The purpose of this study is to find out whether a medicine called zongertinib (BI 1810631) can slow down the worsening of advanced non-small cell lung cancer better than the standard treatment available. Zongertinib may slow cancer cell growth by inhibiting HER2. This would prolong cancer re-occurrence and increase survival. Current standard treatment is pembrolizumab plus platinum-pemetrexed chemotherapy. Participants are put into 2 groups by chance. One group receives zongertinib at regular times throughout the study and the other group receives infusions of pembrolizumab, pemetrexed and cisplatin or carboplatin (pembrolizumab plus platinum-pemetrexed chemotherapy) into a vein. Participants may be in the study up to a maximum of 70 months. During this time, they visit the study site about every 3 weeks for study procedures. The doctors regularly check the size of the tumour with a CT or MRI scan, at the beginning of the study and every 6 weeks. After 18 months they check the tumour size every 12 weeks. Doctors regularly check whether the cancer has spread to other parts of the body. The doctors also regularly check participants' health and take note of any unwanted effects. The time it takes for the cancer to worsen is compared between the 2 groups to see whether the treatment works. The participants also fill in questionnaires about their symptoms and quality of life.