I have heard of some people sharing a LA with a sister, or other relative. I think that's a special circumstance, because they're already used to sharing and working out differences within the family. Sharing with a friend or neighbor would be a different thing.
HOWEVER... all things are possible, if you both approach it with the right attitude and you both want it badly enough. I think a comprehensive contractual agreement is a must. It would need to cover all sorts of things, like what happens if one party moves, or has to sell her interest due to family emergency, illness, etc. Personally, I would not consider doing this, but that does not mean it would not work for someone else. Before you do it, think of everything that could go wrong and how you could account for that in your contract. And good luck!