Prime Time Shuttle can be arranged in advance on-line (at least the return trip from the Four Seasons to LAX - not sure if you can make advance reservations on-line for trips originating at LAX). I believe they give you a discount if you book a roundtrip, and if you belong to AAA. It will cost about $36-$40 for a roundtrip, plus the tip for the driver. And you may end up being the first or second drop-off.

A taxicab will run $35-$50 each way, depending upon traffic & the route the driver takes. During non-peak hours he'll probably be tempted to take the freeway. The freeway will take you on a more circuitous path, and therefore cost more. Tell the driver when you get in the cab to take La Cienega North, make a left on Burton Way, and a right on Doheny. On the way back, tell him to take La Cienega.