D.W.
LAX is surprisingly user-friendly. If your Dad has a cell phone you could arrange to meet him on the sidewalk outside baggage claim you could time your arrival for 20 minutes or so after the flight lands and just pull up to the curb. you won't be able to wait for him there though, so he needs to be on the sidewalk when you arrive.
My favorite method -
Each terminal has its own parking lot. So check the terminal and then just park in that particular lot and walk across to baggage claim and wait for him there. Easy.