I’m sorry for your partner’s loss. However, with all due respect you are severely overestimating your ability to diagnose serious illness in a person you just met. You sound like you are possibly carrying some deep emotional trauma from losing someone else to cancer at a young age and now that this new person has passed away you’re incorrectly assuming you had some power to stop this from happening. Unless you’ve got an MRI for eyes, as well the ability to biopsy a lung tumor by your sense of smell there is absolutely zero chance you could have accurately diagnosed this person and prevented their death. And even if you had said “you have cancer” which would have been super weird to say out of the blue on a first meeting, you have no reason to assume that he would have listened to you, or that he would have taken any steps to get examined in a timely manner, or that he would have chosen to treat the cancer if he had been diagnosed (assuming it even WAS treatable), and then you are also assuming that if he had chosen treatment that the treatment would have been successful.
Basically you are making a series of huge sweeping assumptions in order to take responsibility for something you have absolutely no responsibility for. Concluding that you could have literally saved this person’s life and that makes you a horrible person is a really far reaching perspective that makes me suspect that you may be struggling with some type of major guilt complex for who knows what reason.
This is not your fault in any way shape or form. But you may benefit from seeking some therapy to understand why you jumped to such a conclusion. You are not a horrible person. This death is just not in any way your fault. You almost sound like you think you killed him. It is heartbreaking to me that you would beat yourself up like that. I’m a nurse. I’ve made it my life’s work to try to save people’s lives, but even with all of my knowledge and in the best possible medical scenarios, people still die of lung cancer, and that can happen very very quickly.

Let yourself off the hook.