If indeed you are in a sleeper, in addition to using the lounge to wait for the train once you do return to Penn Station, you can also store a bag in the lounge for free. Don't leave anything valuable there however, as it is unsecured.

I would also recommend planning your return to the station with a bigger cushion than 15 minutes. That could be cutting things close for the LSL, especially if something goes wrong with the means that you are using to return to the station.

And other than picking up your tickets, something that you'd need to do before trying to check your bags as they'll want to see the tickets, there is nothing else that you need to do prior to boarding the train. There is no "checkin" like there is in an airport. There will be a person at the top of the escalator going down to the track level who will want to quickly glance at your ticket to ensure that you are boarding the correct train, but otherwise there is nothing else that needs to be done.

As for Chicago, when you arrive into Chicago the train will most likely pull in on one of the stub end tracks. As you walk down the platform when you get to the end you'll have to turn left to reach the station. Just keep walking straight ahead. IIRC you'll go up a small incline/steps and then the hall will turn to the right. Baggage claim will be on the right inside a big room. They have airport style luggage conveyor belts that the bags will show up on after they're unloaded.