My suggestion:
Due to time constraint, your best bet is to hire a car service that will pick you up from the airport and straight to your meeting in Burbank. (I've done this many times living in Toluca Lake a few years ago and having to jet for same-day meeting flights via LAX.)
By the way, your goal is doable, so don't be discouraged.
With a flight arrival of 8:45a, you will most likely get out of the airport around 10a -- depending if you have baggages, etc. If luck is on your side that morning, you may even get out sooner. Anyway, even with a 10a departure from LAX, you will still make it to Burbank by 11:25a. At 10a, the freeways are more cooperative. Your driver will most likely take you via one of these routes - or tell him if he's not sure:
FASTEST:
1) 105 EAST > 110 NORTH > 5 NORTH.
IF 110 NORTH IS CONGESTED:
2) 105 EAST > 110 NORTH > 10 EAST > 5 NORTH
We have a side-street route we use in our company that provides our drivers with a 90% guarantee of getting there in 50 minutes, but it's too long to give that route here.
Upon leaving your meeting, it's best you hire the same car service (if you had a good experience with them in the morning) to take you to LAX. Your worse case scenario on a typical rush hour drive would be 2 hours. So you're safest time of arrival at LAX will be 8p -- which will still be enough time for your late-night flight.
I've done what you're planning to do many times, and it's gonna be okay. Car service will cost you around $50 each way.
Another solution is to take the Super Shuttle or Primetime Shuttle from LAX to BUR airport. (I know this exists via Super Shuttle, but I'm just not sure of the price.) Then you can switch shuttles when you're at the Burbank airport and head to your meeting. However, the car service may just give you less headache and stress -- and it may end up costing the same at the end.
Good luck, have a safe flight and positive meeting!