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This is something that I have been considering for quite a while based on a fictional story I had read.

An unconscious individual must undergo emergency surgery in order to stabilise them and prevent the patent's death. This medical intervention is happening without the patent's explicit consent however since a reasonable person can be expected to consent to life saving surgery (absent a living will or some other indication) I don't think anyone would have any ethical concerns about it.

However while the surgery is occurring something that would not cause immediate harm but is highly likely to cause extreme disability in the long term is discovered (for example a tumour). Is it ethical to fix this newly discovered condition at the same time?

You're describing an unexpected intra-operative finding. The possibility of unexpected findings (and their treatment) is usually discussed during the consent for the original procedure. Of course, in this situation, there was no initial discussion. The way this sort of issue is usually framed in medical ethics uses a framework of four principles (see Beauchamp and Childress, Principles of Biomedical Ethics): autonomy, beneficence, non-maleficence, and justice. Here, beneficence (the best interest of the patient), outweighs autonomy (the right of the patient to make his or her own choice) for the life saving surgery, and the same would need to occur for addressing the unexpected finding. One would have to (intraoperatively) consider the risks and benefits of removing the tumor, as well as the risks of a second operation were the surgeon to defer. In, e.g., a laparotomy, a readily visualized tumor would almost certainly be removed and sent to pathology. Other cases (e.g., neurosurgery, with a tumor involving eloquent cortex), are more complicated. This sort of thing is less common now, given the likelihood of seeing any tumor that would be obvious during surgery ahead of time with high resolution cross sectional imaging, but it does happen.

You can read a little about the decision making around unexpected intra-operative findings here, in the context of abdominal surgery.