It's been awhile since I've been to LAX, but I don't think so. There are very few toll booths in Southern California, and none that I can think of on any of the interstate highways (only on the "toll roads" such as SR-241, which is farther south in Orange County). There are no tolls on any of the Interstate highways in the LA/Anaheim area AFAIK (I-5, I-405, I-105, I-605, I-710).
SR-91 has some "fast lanes" where you can pay extra in order to use them (which requires a FasTrak), however this is not required, and I don't think there are any toll booths to collect fees, there are transponders that just read your FasTrak. And, at the time I was living there, I think most of those fast lanes were on the eastern part of the SR-91 toward Riverside, which you wouldn't use.
Most rental car companies will have an EZPass (or whatever the local version is) in the car in a box. If you want to use it you're usually charged a flat convenience fee (around $15) plus any usage you incur. If you don't want to use it you just keep it in the box.
I've lived in California all my life and the only tolls I've encountered are on crossing a bridge. Toll roads otherwise would be very rare. I wouldn't worry about it.
I do remember on my one trip to WDW several years ago being surprised by how many tolls there seemed to be, just on regular highways. It was incredibly inconvenient because at one point we got lost and ended up going through the same toll area several times to get where we needed to.
No toll roads from LAX to DLR. I forgot the freeway that you take directly off of LAX (405 or 605) but you can take that to the 5 (or through Torrance to the 91 to the 5) and there aren't any toll roads.
If you go further into OC, like Irvine or Laguna Beach, then there are tolls.