As LOT are *A, they will share the same lounge facilities as LH.
If you have *A Gold status, you can use a Senator Lounge (slightly nicer food and drink), otherwise, you're in the LH Business Lounge.
There are LH lounges dotted all over the Terminal 1 (the LH/*A) in FRA.
You'll be making a Schengen to non-Schengen transit in FRA, so expect to go through German border control in FRA.
Depending on your arrival gate and the LOT departure gate, this could include either a simple pass through German border control, down some stairs and into the Schengen area, or a nightmarish trek which is close enough to going landside and back airside again, including passing through a security screening point.
It really is a toss-up what you might get. You may even have to through additional security screening at the gate itself, depending on the gate. It seems that the arriving/departing pax streams and sterile/non-sterile areas at FRA are a bit of a moveable feast.
So, head for the appropriate pier/gate area for your connecting flight and find the LH lounge complex in that gate area. Get the Schengen to non-Schengen crossing out of the way as soon as you arrive.
The signage is totally variable, from clear and easy to understand, to confusing and woeful.
I used to transit FRA a lot in 04/05 and grew to loathe the place, to the extent that I would try and transit through MUC in preference, and once Swiss joined *A, I switched most of my flying which would involve a connection in Germany to LX and connected through ZRH.
Mike