This is one of the great perks of CL for us. We always take a late flight home, usually 7pm. This way we can check out in the morning, store our bags with Bell Services, go to a park, then return to the lounge about an hour before ME to change, relax, and grab some snacks & beverages.
Last year, after we checked out & spent a few hours in Epcot, DS12 began to feel sick. Our ME wasn't until 5pm, and thank goodness for the CL lounge. While I certainly didn't want to expose him to others if he had a bug, it was the best place for him to just relax in a quiet place. We tried to hang at the pool but it was super hot & I felt he'd be better off in the AC. The CL staff tried to get us a late check-out so he could rest in a room, but the resort was booked solid. They were super nice about checking on us & seeing if we needed anything. There was one CL CM that just babied him & kept feeling his forehead & talking with him, it was so nice, she sure didn't have to do that!
(Ends up he was just nervous about the flight home!)