Mark,
I don’t think that there are any directional signs pointing to the lounge, only to the general waiting areas. However, the following should help you to find the lounge.
The Chicago Metropolitan Lounge is located on the lower level of Union Station, which is also the track level. If you are standing in front of the Amtrak ticket windows, then the Amtrak waiting area is to your left. When you enter the main Amtrak waiting area through a sliding glass door, just walk forward and slightly to the left. There should be another sliding glass door along with a sign, unless they've changed the entrance in the last few months. Show your tickets to the attendant and they will give you a pass to come and go as you please. Or you can just stay in the lounge and relax.
The Chicago lounge can be very busy and it sometimes can be hard to get a seat during the mid-day hours, but after 4:00 or so things empty out some. Note: They will make you leave your carry-on bags in either the luggage room inside the lounge or a small locked room down the hall. The attendant will direct you in this matter, but you cannot take them to your seat due to the crowded nature of the lounge. Do not leave any money or medicine in those bags, take it with you. They’ve never had any theft problems that I’ve heard of, but there have been a few instances over the years, of someone grabbing the wrong suitcase.
In New Orleans, the lounge is very small and last I knew there were no signs at all. You just check in at the ticket counter and they will direct you to the lounge. It’s located directly opposite the doors leading to the tracks or almost directly behind you on a very slight diagonal when you’re standing at the ticket counter.
You will get dinner out of Chicago if you want to wait for it. Of course you are free to eat on your own inside the station, but it will be on your own dime. If however for some reason the train is late leaving, then the attendants will give you vouchers to buy a meal in the station.
Leaving New Orleans, you’re on your own for lunch. Lunch will not be served in the diner to my recollection. You could of course buy something from the café car, but I’d probably suggest eating before you arrive at the station. There are a few places to eat in the station, but the selection was very poor the last time I was there 2 years ago.
Have a great trip!
And please be sure to come back and tell us how things went.