Is there anyway I can get my house carl, Lydia back?

I've looked everywhere, the breezehome and dragonsreach. In the breezehome it says the bed for Lydia is still owned. In an earlier quest Lydia got killed by a powerful mage, which I killed by a sneak attack. I've went back multiple times but she still lays there dead. I now have a follower Jenassa, and it said I don't have anyone. So is she dead completely and won't be coming back. Or is there a way to bring her back?