That's not what the rules say. https://www.lufthansa.com/de/en/admission-rules says "entry to the First Class Terminal in Frankfurt is only possible with a confirmed First Class flight on the same day with Lufthansa, SWISS or Discover Airlines" (it's the 1 condition by FCL/FCT, so I assume it applies to both). However, Star Alliance has a different rule, which is lounge access only if qualified on departing flight, which prevents people connecting in business using the Polaris Lounges in the US for instance. I think confusion about the different rules leads to the impression (enforced sometimes on entry) that you must be arriving or departing that airport in F, but if you point to a copy of the page and press your case you might get lucky.