I've done this relatively recently, incoming domestic flight into T6 around noon, outbound flight LAX-BKK in the evening from TBIT. In my case, I just arranged for a rental car, picked up my stuff at the T6 baggage carousel, then took the shuttle over to the lot, stuffed bags in trunk, and off I went tooling about for the next 8 hours. I wasn't travelling too heavy and didn't want my stuff hanging about in LAX baggage area, so preferred the recheck-option to interlining. I think I allowed enough time to get back to TG check-in a couple of hours early.

Nobody cares if you leave LAX during transit, but it's up to you to get yourself back to appropriate area to do check-in and/or security.