Thank you all. We definitely want to be done with security AND passport control before we settle into a lounge. So your posts were most helpful. We'll probably go to Eventyr to try that.

One time in Milan flying BA I think, the lounge is right next to passport control, but still before it. So since the lounge is right next to passports, we had plenty of time, right? No. The lounge agent never announced our flight was boarding (though she promised a dozen times that she would). We finally left the lounge and there was a huge line at passport check, and we saw our flight boarding. Panicked the entire time we were in line, but we made it.

So for me, I won't relax in any lounge until I am done with security and done with passports. Thanks again