Once your tank is established and stocked, live rock is pretty self-sustaining. It is called "live" because of a variety of organisms that live on it. Because of that variety, there is no one food need. One of the main reasons we use live rock, for instance, is the biological filtration provided by bacteria living on the rock. The food used by the bacteria comes from the waste of tank inhabitants and the breaking down of left-over/uneaten fish food. You might also find various fan worms, polyps, or other creatures living on your rock in time as well. Some of these feed photosynthetically, others filter what they need out of the water, and some are scavangers living off the
detritus that accumulates on/in the substrate. Bottom line to all of that is, there is not much you need to actively do for the live rock once it is cured and you have livestock in the tank.