"He has lived in the home since he acquired it. My dad had the home placed in my name and put himself and my mom as lifetime interest 15 years ago. We were talking about doing some work on the home but did not get to it yet."
I'm no expert, but it was my understanding that the holder of a life estate in a property normally has the duty to maintain the property so the remaindermen receive it in at least the condition it was in when he acquired the life estate. That would mean that fixing things that are broken and replacing things when they wear out are perfectly normal and legitimate expenses of homeownership, and Medicaid should have no problem with those.
If Dad proposes to spend his money adding things that change what the house is, going beyond just keeping it shipshape, those expenditures might be questioned. I don't know. The thing is, as long as he lives in this house, it's his house, so it's quite possible that Medicaid might view it the same way as if he had not given you a remainderman's interest in the house and it was still just his house.
If Dad's money stretches beyond maintenance and repair, I think you and Dad should consult an elder law specialist with knowledge of both the legal ins and outs of spending down his money and of the real-life quality-of-care consequences of doing so. Ask about ways to keep some money available to him for care extras, if that's possible. A private room, even just for a while, can make a huge difference if he happens to be sharing a room with someone who makes noise all night or otherwise makes it impossible for him to get some rest.
My father spent his last 2 weeks in a Medicaid-accepting nursing home in CA (the hospital sent him there supposedly to finish his recovery), and the place seemed awful in general, had no reasonable phone service for the patients (I literally could not understand a word he said, the reception was truly awful), and we can't prove anything but his neighbor who visited him there noticed several things that suggested they accidentally gave him the anti-psychotic medicine meant for the guy in the bed next to his.