Print out your A3 account page as suggested by WineCountryUA
While this might not work in 100% of all cases, it worked for me to get access in MOST airports while I waited on my cards.
DO NOT FORGE/FAKE ANY LETTER! I'll have absolutely 0 sympathy for anyone getting catched doing so and smuggling themselves into the lounge with a forged document. If you've access, print out your status, it shows at which date your status got updated, and if that's within 8 weeks or so, you should be able to reason your way in.. (and, of course, if it's longer and you lost your card, you might also try this - don't fake any documents!)