In the past couple of years, I've always been asked what train I'm riding on. Sometimes, especially in Washington, they even check, taking my AGR card and running it through the computer. This last week in Philly, I just flashed them my card; they asked me what train I was riding, but didn't bother to take the card to see if I was legit. It seems that their main interest in Philly is to know who's riding which trains so they can know when to operate the elevator to the platform. (One of the best features of the Philly Lounge, by the way.)
Back in 2001, my brother came to the Chicago station to see me off. They were fine with his staying in the lounge with me, but that was over 20 years ago, so who knows what the policy is now.
Basically, it's typical Amtrak - policy made up on the spot by the whims of whoever has authority that day. That said, I don't see any reason why they shouldn't let a non-traveler stay in the lounge to see someone off. The only exception might be Washington between, say, 3 PM and 7:30 PM, when the rather small lounge gets filled with evening NEC commuters and sleeper passengers from two long-distance trains, and of course, actual travelers should be getting priority.