Unfortunately your arrival time and meeting time will put you in rush hour both ways. Yes, it's doable but plan on at least an hour or more in traffic each way. Car service is a good idea but I am not sure where you will find one for $50. My house (which is 3 miles from BUR) to LAX is $75-85 each way with everyone I have ever checked/heard of.

Definitely rental car. Definitely get one you don't mind sitting in for along time. You won't miss your flights, but you will be on the freeways for a good amount of time. No need to reschedule your trips though.