If you miss the 6:05pm LAX-TUS flight, you will have one more flight that night at 8:40pm. From what I've read/experienced, WN is pretty forgiving regarding about missing a flight and putting you on the next one. It all depends on the GA, so YMMV.

As for the drive from SD to LA... depending on time of day, with no traffic I usually make it within 2 hours, at an avg speed of ~75mph/120kph on the freeway (topping 85mph/136kph). The legal speed limit on I-5 is 65mph. Hindrances are traffic (which can be bad both out of SD and starting in Orange County) and as such it really can be hours more; and the customs checkpoint... if it's open, it may add 5-45 more minutes to your drive.

The most direct route SAN-LAX is the I-5 North to the I-405 North.

But I'm gonna guess that you want to drive up along the coast and see Southern California's finest? If you're adventurous, I would recommend this route from SD (routed from SAN airport):

-North on the I-5.
-Take I-8 West.
-Exit Mission Bay Ave. NORTH (turn RIGHT)
-Follow signs to continue on Mission Bay Ave. (if you go straight, you'll end up on Ingraham).
-Street will turn into Mission Blvd.
-Turn LEFT onto La Jolla Blvd.
-Street will turn into Prospect St.
-Turn LEFT onto Torrey Pines Rd.
-Bear LEFT onto N. Torrey Pines Rd.
-Street will become Camino Del Mar.
-At Jimmy Durant Blvd, bear LEFT to continue on Camino Del Mar.
-Street will become Old Hwy 101.
-Street will become 1st St/S Coast Hwy 101.
-Street will become Carlsbad Blvd.
-Street will become Coast Hwy
-Take the I-5 North
-Exit Avenida Pico in San Clemente.
-Turn LEFT on Ave Pico.
-Turn RIGHT on El Camino Real.
-Follow the signs for Pacific Coast Hwy (PCH) aka Hwy 1.
-Turn LEFT on Westminster/2nd St. in Long Beach.
-2nd St. turns into Ocean Blvd.
-Continue over the Vincent Thomas Bridge, and take I-110 North.
-Exit Anaheim Blvd., turn LEFT, the LEFT again onto Anaheim.
-At the 5-way intersection, bear LEFT onto Palos Verdes Dr. N.
-At a Y-split, bear RIGHT onlto Palos Verdes Dr. W.
-Continue straight, onto Catalina Ave.
-Turn LEFT on Beryl/Hermosa Ave.
-Street will bear right and become Hermosa Ave.
-Turn/Bear LEFT onto Manhattan Ave.
-Street will become Vista Del Mar.
-Turn RIGHT on Imperial Hwy.
-Turn LEFT on Sepulveda.
-Follow signs to LAX.

The route I gave you above is mainly surface streets, with traffic lights and all, so will add considerable time to your drive. But you will drive along the coast and hit some nice places: Mission Bay, La Jolla, Torrey Pines, Del Mar, Carlsbad, Oceanside, Dana Point, Laguna Beach, Newport Beach, Huntington Beach, Long Beach, Palos Verdes, Redondo Beach, Hermosa Beach, and Manhattan Beach. Also lots of turns I left out that could be interesting (e.g., taking the ferry between Newport Beach and Balboa Island).

I hope this helps.... welcome to SoCal! ^