Jenikaye,
One final thought that I just had, since you are traveling in a sleeper to Chicago this qualifies you as a First Class Passenger. This typically means that you have access to all of Amtrak's first class lounges. On the east coast they are called Club Acela, elsewhere they are called Metropolitan Lounges.
Anyone traveling in first class is entitled to use these lounges to await the departure of their train or when connecting to another train. While there are no lounges in California, there is one in Chicago. Even though you are not traveling in a sleeper or first class from Chicago to NY, since you rode first class on the Chief you are still allowed to use the lounge in Chicago. Just show the attendants in the lounge your ticket stubs from the Chief along with your tickets for the Lake Shore. They should allow you to wait in the lounge for your departure. Below you will find my usual description and directions that I normally give to anyone using first class. I didn't think of this originally since you were leaving from a station that does not have a lounge. Sorry.
Your sleeper tickets qualify you as a First Class passenger on Amtrak. As a first class passenger you are entitled to utilize Amtrak's first class lounge in Chicago. These lounges are a nice quiet refuge in the often-bustling train station. They have nice plush chairs, conference rooms, computer terminals, newspapers, TV's, free soft drinks, juices, coffee, tea and clean safe bathrooms. They also allow you to board your train before the rest of the masses.
In Chicago the lounge is called the "Metropolitan Lounge". It 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. Again, just show your tickets and relax. Note the Chicago lounge can be very busy and it sometimes can be hard to get a seat, but you still get the free stuff and priority boarding. Note: They will make you leave your carry-on bags in the luggage room inside the lounge, you cannot take them to your seat due to the crowded nature of the lounge.
I will also mention that there is a locked luggage area for first class passengers. You can find this room by making the first right after you walk through the first set of sliding glass doors that I mentioned above. Walk down a short hall towards the south waiting area and again make the first right available. This is where I usually leave my bags when I go through Chicago, as opposed to the unlocked side room in the actual lounge. I’ve never heard of any bags being stolen from the unlocked room, but there have been a few cases of people grabbing the wrong bag by accident. Note that I have not been in Chicago since 9/11, so it is possible that due to security reasons this locked room may have been closed.
Also never leave any valuables in your luggage or your bedroom when you are not there. Take all wallets and purses with you, when you are moving about the train. There are usually no problems, but don't tempt the fates. Also don't leave any important medicines in your luggage while in Chicago, keep it with you.