Miles & More (Lufthansa, Austrian, Swiss, and other partners) - Lounge Access Question

Flying BOS>FRA in J on a 2 class A340 departing 10:30 pm.

Arriving FRA next day and connecting to FRA>NRT in F with 3 hour connection in FRA.

Do I get LH IFL access in BOS. Agent said no but let me in anyway.