I believe, but I'm not positive, that it is possible for you to leave your bags in the NYP Club Acela lounge for the day. But if you do, know that the bags are in a common, unlocked room that anyone in the lounge can access. I think it highly unlikely that your bags would be taken, but you do need to understand that there is always that chance and that no one at Amtrak will be responsible for them.
If you do leave them there, I highly recommend that you make certain that they are well tagged and perhaps even have some unique marking or colorations on them, so that there is less chance that someone accidentally grabs your bag because it happens to look like their's.
If the attendant tells you no, or you decide not to risk it, there is always the day checking. But that is a bit expensive IMHO, last I knew it was 5 bucks per bag.