Been Jammin,
I lived in L.A. for over a decade, so I know quite well how limited access and egress are, but there actually a few more options than one or two, depending upon where you are located in L.A. County (remember, we're talking about an area that is 4,750 sm - OK County for reference is 718 sm). There are actually quite a few surface roads that can get you out of the city, you just have to do a bit of zigging and zagging.
But here's where it gets stupid, why would they count on getting water at their destination, or there even being a place available to them? Do they think they're going to be the only ones who have had a similar bright idea to head to the desert to insulate themselves from a virus? (They kind of an idea there is a virus or similar that is causing this.) Are they living in some parallel universe where the incredible problems of trying to evacuate to deal with the aftermath of Katrina never happened? And New Orleans only had a population of around 450,000 at that time, the population of L.A. Metro and surrounding areas is more like 14,000,000. Accommodations out towards the desert area east and southeast of L.A. are incredibly sparse to begin with, even a few thousand others headed that direction would eat up all the rooms and resources.
Sorry, if pimply faced teenager can figure out the necessity of stocking up on food, water and essentials, I would expect someone who has a bit more worldly experience and education to at least be able to grasp the fundamentals of a "bug out." You don't have to be a devotee of "Doomsday Preppers" to understand that in a survival situation, water is the #1 priority by a long-shot. You can a week or so without food, your typical max time without water is about 3 days in an arid climate.