They might stamp your BP at the LX lounge when flying with *A carrier (except LX, LH, OS) because of lounge agreement? LX lounge (handled by Swissport) will charge every single lounge entry to the responsible airline. Maybe LH lounge will do so too and the airlines aren’t willing to pay twice or even three times per pax. If this works – I don’t know. At least it will harm the passenger not to go lounge hopping… Now don’t blame me on my thoughts, it’s all just an assumption!
Bellevue Lounge is located Dock E West and US flights depart form Dock E East. I know security east checks BP (to make sure you fly to US and don’t carry on any explosive water - smile), but does security west also check your BP? I once used Bellevue lounge when travelling to US and had no problem passing thru; although they checked my BP but only told me not to forget to change terminal (West/East).