L337,
I can't speak for LAX but here at IAH and in most of the US the FARs require a speed of 250kts below 10,000, and a controller can not delete that without a waiver which LAX may have, I'll check for you. We had a waiver a few years ago but departure control used set phraseology to delete the speed. That experiment (the waiver) did not work out here due to overtake issues and other safety issues.
Regards, CZHU