Originally Posted by PetzLUX

You can access the LX F lounges (A and E). Keep your F boarding pass and show it at the lounge entrance.
FRA-ZRH can be LH or LX, no problem.
Your flight from FRA will arrive at A/B and your flight to ATH will also depart from A/B. So going/coming to/from E requires you to pass passport control twice and ride the Heidi train twice. No problem if you have enough time.