they are certainly not going to know whether or not you are there. but, i thought there was a 4 hour rule on checked baggage for a layover, meaning if the layover is over 4 hours, then you have to get and recheck bags. if you're leaving lax for the day, are you getting a car (how else would you get anywhere in la?)? in that case no problem. and finally, i seem to recall a place that opened nearby lax that does checked luggage, but don't have details.