4 hours to Lone Pine from San Diego (North County) would be under ideal road conditions. The fastest I think I've ever done that trip is 4.5 hours and I travel from Poway, which is just a few miles south from you.
To better acclimate I'll usually go straight up to Horseshoe Meadow and spend the night there. Hike in the morning and head down to the Visitor Center in Lone Pine for a permit. Then spend the next night also up at Horseshoe Meadow, near 10k feet.
Your next trip up Mt Whitney should be easier now that you've been on the trail and know what to expect.
