Arriving at Heathrow requires going thru immigration control, then security as soon as you land, before you can get to the next flight, whether in a different terminal or even in the same terminal. Having to change terminals certainly adds to the potential dilemma. Having the flight land on-time at Heathrow (or even early?) could make all the difference in making the connecting flight. Be prepared to notify airport staff of your situation - we’ve gotten bumped up in the security line when we had a late flight and tight connection.
This is from the British Airways Website:
We recommend that you allow the following minimum connection times:
1 hour for connections within the same Heathrow terminal
1 hour 30 minutes for connections that require travel between terminals at Heathrow
So that airline suggests that 90 minutes will work, but don’t delay getting off the plane, thru immigration/passport control, then thru security, and on to the other terminal. Again, look for an airport official if you need help.
Worst case scenario, get yourself a new paddle (ticket), if you don’t make the Lufthansa connection and are up the creek at Heathrow. There’s a BA flight tomorrow evening (not that there’d definitely be one with available seats the day you land, but at least there appear to be options) directly to Hamburg, less than $150. Maybe a same-day flight would still get you to your final destination, and not cost an arm and both legs.