Depending on how late one arrives at LAX, I'd recommend more than an hour. Flying JFK-LAX-SBA, on several occasions we arrived at LAX an hour or more late, and missed the last AA flight to SBA (think around 10:30pm). Had to overnight in a hotel. First flight out the next day is around 8am (and you get to go through security again).

FWIW, when I'm traveling in/out of SBA during winter months and June, I connect at LAX on the inbound and SLC on the outbound. The flight to SLC is long and on a RJ, but have never had any issues with it missing my always tight connection in SLC. (Also depends on time of day...I personally place more value on the non-breakfast transcons in F).

Also depending on the time of day one arrives at LAX, I'd not recommend driving. Aside from allowing 30min minimum to get the car (and I have Hertz#1 Gold), if you arrive around pm rush hour, you'll be driving to SBA through some of the worst traffic in LA. If you arrive later than that, you'll be pretty tired on the drive to SB. The drive up PCH/Rt 1 is very nice, but you have to consider that a leisure drive, and not a quick way to get from LAX to SB.