You cannot work for them simultaneously. If you want to work for X/Y, and X/Y has not withdrawn the petition, you can work for them. If they have already withdrawn your petition, then they will have to file another petition for you to work for them (this will be cap-exempt).
Also, you are currently working on L-1. So in order to work on H-1 COS needs to be filed. It can be filed along w/ new petition or separately (if an old petiion is being used).
Yes, there is concurrent H-1 but like you said only if you can satisfy both the LCA requirements. In case of concurrent H-1, one of the H-1s is typically part-time while the other one is full-time.