Well, you're going to be a little disappointed. Neither AA nor UA offer lounge access to frequent flyers on domestic routes. DL does, if you reach Diamond level and choose that benefit; however, DL has many fewer nonstop destinations out of Chicago.

Both AA and UA sell lounge access, and lounge access is included with various credit cards (but check to makes sure the airports you'd be using have a lounge that you can enter with a given credit card).

You can get lounge access on UA domestic flights by accruing Gold status on a Star Alliance partner. You wouldn't get any other benefits, but if that's the most important thing to you, it might be worth considering. Aegean and Asiana have both offered reasonably quick paths to Star Alliance Gold in the past. It will be extremely difficult to get Gold status on your Miles & More account by flying UA domestic fares.