Just to add:

You access the Senator Lounge by a little door near the security check of terminal 2. You'll find it by walking along the pier/concourse as long as you are at the position of terminal 2 and see a sign "lounges". There you will recognize "LH Lounges" and "BA lounge" signs above that door/elevator. Take the stairs/elevator one level up. Walk along the hall, pass the Airport Lounge and the BA lounge until you arrive at the LH lounges at the end.
To get back to the baggage claim/exit, you have to go down again and follow the signs "exit terminal 2" in the pier.

I hope, that will help.

Which flight/airline are you taking into Hamburg? I might help you with some
more descriptions if I know the flight number, because some airlines/flights always arrive at the same gates.