Hello, Maurice and welcome.
First, you can contact TSA's Lost and Found at LAX, to find out if they have your driver's license:
TSA Lost & Found
5757 W. Century Blvd., Suite GF06
Los Angeles, CA 90045
Hours of Operation: 7:00 am to 7:00 pm PST, Mon - Fri
"Since TSA has taken over the responsibility of passenger and checked baggage screening, all items left behind at security checkpoints are logged, collected and secured. Once passengers contact the TSA Lost & Found to claim and verify their item, arrangements are made for in person retrieval from 5757 W. Century Blvd."
You should be able to fly back to LAX tomorrow, by either showing other forms of acceptable ID (listed below) at the TSA screening point or after telling them that you don't have your license and why, they can check publicly available databases from the information you give them and/or other ID you may have, to clear you to fly. Passengers forget or lose their licenses all the time and TSA understands this and will do everything possible to help you get on your flight, so I don't think, under your current circumstances, you have too much to worry about. However, do arrive at the airport earlier than usual, to allow time for this additional screening, since you don't have your license. Tell your airline, when you first check in, about the license not being returned to you at LAX security screening.
Here is a list of acceptable ID's from the TSA:
Here is the TSA Contact Center's information if you need to get in touch with them:
8 a.m. to 11 p.m. ET
9 a.m. to 8 p.m. ET
I wish you much good luck in finding your driver's license and safe travel!
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