You should be able to leave the airport, however I don't think you'll have enough time to do what you plan...
the flight arrives at 9:40? assuming it's on time, that's when it lands... not when it gets to the gate, I've been in/out of LAX with 30 minute taxi times before.
You have to be at LAX 2 hours before flight (it's one of the few airports where that was needed before 911 because of the queues and distances you have to travel between checkin and the gates)
Getting in/out of LAX can take hours in traffic.
If you're lucky, a 13 hour layover will give you 3 or 4 hours to do your errand.
As long as you don't get lost (don't rely on a taxi driver), you might get your fingerprinting done... unless you have to wait when you're there. I had to have mine done at the police station, and had to have an appointment, and then it still took all morning to get it done. The actual fingerprinting took about 5 minutes, but I waited in the office for 2 hours before they would do it, even though I had an appointment.