Refer to the "this week" link at ocdance.com . Nancy Lester does a good job of listing just about everything dance-related that's going on in LA, Orange, and other surrounding counties.
"LA" covers a lot of territory; which area are you mainly interested in? I'm primarily OC myself, never wandering into LA without my Thomas Bros. Most recommendations I could make would be OC-centric. The good news appears to be that the amount of instruction in country dances is increasing.
One thing you could do would be to visit country venues for leads. In the eastern part of the county are Cowboy Country and (I think it's still there) Wild Horse in West Covina. I think Louis Herrera teaches at CC, though it's been a while and I've lost track of him. Of course I would recommend Jack Berard, but he lives in South Orange County.