If I were an employer, I would think that it is my business. I want to understand why someone has a gap. OP doesn’t need to go into any detail and can just say “medical reasons that I’m completely recovered from and no longer apply to any position” and leave it at that. But lying is a bad strategy because they’ll either need to maintain the lie forever or the truth will come out. And it’s hard to have a good lie. If a candidate says they had family related work gaps for four years then that will place them poorly compared to candidates that don’t.
I’m of the belief that even though employers may lie or be deceitful, I don’t want to be. I understand that puts me at a disadvantage and I accept that trade off for “doing the right thing.”
I also look for companies that don’t deceive like this and don’t want to be in a situation where I try to explain that I only lie to bad companies and promise not to lie to them.