Hi martinfoss, welcome to FlyerTalk. First off, your best bet to get from Universal to LAX would be on one of the shuttles. Taxi fare would be huge. Secondly, it's a real crapshoot on the time. If you're leaving on the weekend, you're in better shape- probably about 75-minutes. But if you're leaving on a weekday, you'll be right smack in the middle of rush hour traffic on the busiest interchange in the U.S. And anything can happen. Are either of these an option?
1. Fly out of Burbank Airport? It's only several miles from Universal and will save you time and sleep.
2. Would your travel permit you to do your thing at Universal, then check into a hotel near LAX the night before your departure?
If neither of those alternatives work then, if it was me, I'd leave the hotel about 4am to get into the LAX area and then stop and have a relaxing breakfast at the Embassy Suites. Then catch their shuttle to the airport 5 mins away. Personally, the last thing I need before I travel is the stress wondering if there's going to be a problem with traffic, etc. I'd much rather leave way too early than a little too late. JMHO