I wouldn't count on them to check your bags through and even less printing an onward boarding pass if it's on two tickets. I would go the safe option and book a 3-4 hours stopover. You will be glad in case of delays, and if you need to go landside and recheck it can take up a lot of time, especially if you fly US as they're in another terminal than LH.

The Minimum connecting time shown by the user above is never ever doable on a T1 to T2 nonschengen connection. The problem with ITA is that is shows the general MCT loaded by the airport in the GDS, but airlines are loading their own MCT, and they can considerably differ. And they would not apply to you if you travel on seperate tickets anyway.

If you have too much time, better spend some time in one of the numerous cafes and restaurants, T2 has very nice views to the airfiefd too. You will not get bored in FRA.