Just did a similar transfer, arriving on LH from Budapest a bit late, so that I had 50 minutes to then make my UA flight to San Francisco. Walking fast and with no wait at security, and having gotten my UA boarding pass from LH in Budapest, I'd say it took me about 30 minutes--I made it with about 10 minutes to spare and was not the last to board the plane. (No check-in baggage, so I can't comment on how well interlining will work out.) Whether you can do the same might depend on whether your arriving and deparing flights are in the same terminal. Both of mine were in Terminal
1. I had to get from section B (?) to section C (?) within the terminal, hence a fair amount of fast walking. I don't know FRA that well either, but suspect if you have to switch terminals things could get tight.