I lied in an interview on accident. How can I save this?

I have a misdemeanor on my records for petit theft when I was 18. (almost 4 years ago.) It's the only thing I have on my records and I sort of forgot about it. I was in an interview today, and when I was filling out the application I didn't see the part where it asks about your crime history. When she looked over it, she asked me if I had any past crimes, and I said no. I had to fill out this form giving her information so she could do a background check on me. She said she wouldn't get the background check back for another 5 or 6 days, and she would give me a call then. When I got home, I remembered about my misdemeanor. I think I have a chance at saving this job. I want it so bad! It's a job at a high-scale new apartment complex. I don't know what their policy is on hiring people w/ a misdemeanor, but if it is allowable I'm sure I can fix it. Any suggestions?