It would only take a one hour delay on your first flight (headwinds? delay in the US?) for you to miss your ongoing flight so I would definitely allow longer.
United and Lufthansa are both members of the Star Alliance frequent flyer programme. If you have pre-booked your Lufthansa flight, you should get your boarding pass for it when you check in at the US airport and your luggage will be checked through to your final destination (but check where you will have to customs-clear it ; it depends where you are going to from Frankfurt).
I've transited Frankfurt in less than an hour on a Star Alliance through booking. If yo are not booked through with boarding pass, you have little chance.
Just make sure you are arriving and departing at the same Frankfurt airport. Besides the main one there is also Frankfurt Hahn Airport which is miles from the other one (about a two hour bus journey). Hahn is usually where all the budget flights arrive and depart.