Live rock needs zero light, zip, none, nada. It's only the algaes that live on it (desirable coraline, then the "undersirable" algaes) and any possible hitchhiker corals (also aiptasia, hydroids and similar - pests) that need light. So depending on how much/if you want those organisms to thrive/survive, you may not need light/might want more light. But still I would expect you to get some decent coralline growth over time and maybe some other photosynthetic organisms, if they make it into your tank (BTW - aiptasia WILL grow and multiply in your tank, if you find aiptasia, kill at ASAP).
Still some better lighting wouldn't hurt... even though there's no real need for it with your type of tank, IMO a brighter tank looks better.