I'm sure that the U of Chicago must have a deadline for the first deposit...so just give LECOM some time to process your information before signing up for Chicago. If you already interviewed at LECOM, their turn around time is about two weeks (that's what it was for me). And if you go into an interview with one acceptance, it weighs in your favor of getting accepted to another school. If your deadline for Chicago is approaching and you haven't heard back from LECOM or if you haven't interviewed yet, call them, tell them your situation and I'm sure they would consider getting you in for an interview or reviewing your final file quickly.
Good luck!