Since the lapis is going to be essential for enchanting tools, having a few tossed into your inventory every week wouldn't hurt but I don't think it should be half a stack or anything like that. Maybe just a few lapis pieces (3-5) if that, diamond tools last a while on their own and with unbreaking enchants they'll last forever. I think the best thing to do is add a new challenge under expert such as the emeraldcollector, where its a difficult challenge to complete but rewards you with a few lapis pieces.
