If you perform a search in FlyerTalk's SWISS forum on the word "Allegra", you will find a wealth of information on the lounge.
I'm not sure of the status of LX being merged into LH, but you very well may have rights to use the Allegra lounge (if travelling in a premium cabin and/or if you're a top-tier elite). Otherwise, as mentioned, there's a cash payment optioin.
One nice thing is, when you are finished, the lounge staff will escort you back into the airside portion of the terminal.