I assume you're talking about Homewood, IL. The lots around the station are privately owned, designed for Metra commuters. I'm not sure how they handle overnight parking, but you might check with the Amtrak agent at Homewood. They may have some special accommodations for Amtrak passengers. The lot on the east side of the tracks is permit parking only and they're not shy about towing away anybody who doesn't have a permit. The west side lots (on the Amtrak station side) have coin operated gates.