My bf's father

I never had any particular connection with him. He was friendly but I felt awkward. He looks like my bf just with grey hair. Sometimes I think that my bf even old will look like a gentleman (and he will have hair lmao).

He texted me and asked me for a dinner. He said not to tell my bf. I felt weird but I did it. For a moment I thought there would be a scene from a soap opera "lemme get you a check to leave my son, how much do you want". But he was just asking me if we get along and he was asking some things about me, nothing too personal.

And then he told me that he worries a lot about his son because he doesn't have any siblings and he asked me to promise him that if something happened to him I'd be there for him because he doesn't want him to be lonely. He said that he'd like me to consider him as a friend.

Should I tell my bf about this? And the way he told me about taking care of his sons made me worry that his father has a disease or something.