If you want to be friends again (JUST friends) with LA girl, you need to be extremely explicit that you are only interested in friendship. I ended up lurching into a mess of pseudo-relationship bullshit where neither party was sure if we were going out again or not. You should be upfront that you have a new girl and that you are no longer romantically interested in LA girl.
It sounds like that isn't the case, which makes me think you shouldn't talk to your ex until that is the case. If you are still romantically interested in your ex, friendship is a bad idea and planning on using her in case your current relationship goes south is a really bad idea.