What you have is a Stylaster or Distichopora species, sometimes reffered to as "blue fire coral" (as they resemble the shape of commonly seen Millepora sp., a.k.a. "fire coral"), also sometimes reffered to as "lace coral". Both genuses are non-photosynthetic and require minute particluate matter to feed off of, likely needing to be continuously fed as with Dendronepthya and Scleronepthya species.
Lighting is unecessary as they're non-photosynthetic, feeding is still trivial (in that we don't know exactly what they eat in the wild) so your best bet is to offer various foods continuosly dosed, and thriving, well... good luck! There are several of the most skilled non-photosynthetic aquarists in the world attempting to keep these long term and they have a thread going on RC in the non-photosynthetic forum. Unfortunately there is no reports of long term success with either of these genuses.