"I would listed as the owner . . ."
You're not just "listed" as the owner. You ARE the owner.
"if the mortgage is in my name, a no go?"
It's a no-go if you might ever want to buy a home of your own. You also have to consider things you don't like to think about or that you think will never happen. For example, what if something happens that causes Dad to stop giving you money for the mortgage payments? Any of a number of unexpected things could happen that makes him unable to continue, or you could have a falling out. (It happens.) You're still on the hook for the payments. The mortgage could be a 30-year commitment. You can't predict the future.
One tax-related problem that occurs to me is that the tax deduction for mortgage interest is lost. Your father can't deduct it because he doesn't own the house and he's not making the payments. You can't deduct it because it's not your home.
"If he puts me as the owner, but the mortgage is in his name, it's okay?"
The lender won't do that. Your father can't mortgage a house that he doesn't own. They will only lend to the owner of the property.
"We are meeting with lawyers tomorrow. Should I go in asking anything specific?"
Explain to the lawyers exactly what the issues are that prevent your father from buying the house himself, and ask them to suggest a solution.
Ask them to explain any possible estate and inheritance issues. What happens if your father passes away? What happens if you pass away before he does? Again, all kinds of unpleasant things can happen unexpectedly, and you can't predict the future.
What happens if you get married? What happens if your father gets married?
Ask about property maintenance and liability issues. You're the owner. If the town issues some sort of complaint against the property, you're responsible. If someone falls on the sidewalk in front of the house, you get sued.
Ask about other considerations that you don't like to think about. For example, what happens if your father can no longer live alone and has to go into a long-term care facility such as assisted living or a nursing home.
You should discuss the plan with a tax professional in addition to the lawyer. You can ask the lawyers about income tax and estate tax considerations, but lawyers often know less about taxes than they think they do. You also have to consider state income and estate taxes, and state inheritance tax if your state has one.
One other thing to think about, and to discuss with the lawyers. Is there anyone who might object to your father turning over significant assets to you? Your mother? Any siblings or half-siblings of yours? Any past or present wives of your father? Things could get ugly if someone else thinks they have a claim to some of those assets.
