LH (at point of original) has always been able to print my boarding passes for UA flights out of FRA because their computer systems seem to be in synch.

One time in HAM, I was surprised when LH printed a red boarding pass, and that's how I found out I had been upgraded on the UA flight.

55 mins in FRA can be plenty of time....or can be an hour too short. It's nothing you can control; just head towards the gate and don't dawdle.