When you click on the link that you provided and choose "First Class" and "Frankfurt," the following is the result:




It's quite clear to me that the only F-lounge available is in the Schengen area. In the non-Schengen area, only the Senator Lounge B and Senator Lounge Z are listed. So, in my view, I believe that LH is clearly informing you that if you can't access the Schengen area, you'll only be able to visit two Senator lounges, not the First Class lounge and not the two Business lounges.