Not sure what an 'organic' sheep/lamb would entail.
Sheep are free range in most cases from what I can see, they roam freely around paddocks, or often large rural properties foraging for food. I also note that in hard times (when it is dry) they are fed some large round bails of hay (I been told they cost about $20-30 per bail, I only asked the farmer where I buy my hay when I need it, as a horse feed bail will cost around $120-150, hoses won't eat the cheap stuff), not sure what sort of hay it is the sheep eat, but almost looks like straw to me. I don't believe any of the sheep around here are fed grain or anything other than these large hay bails or what ever food they find around the farm.
I also know that they will eat weeds and other vegetation (not just grass) that horses for example won't touch or even look at.
Only reporting what I see around me every day, have not thought about it too much. Also all these sheep out here are for eating not wool production.