I've got a spare VPN hosting plan, and I was contemplating running a lightning node on it. However, it looks as if I will have to run a full Bitcoin node alongside it, so the storage cost would rule that out.
How about running a pruned node instead and determining how much storage space you want to give to the node yourself. I remember reading a long time ago that it was possible to do with the lightning network as well, but it required some extra configuration. People who know more about this than I do could certainly help you.