
He'll give it the maximum number of sockets it can have, which depends on item type and item level (which is hidden, but can be inferred if you know what monster dropped the item). Larzuk is occasionally, if infrequently, a good choice for socketing a white item.

The Horodric Cube recipes only work for non-superior items, which makes superior items with less than max sockets valuable, if they have the correct number for a popular item. There are two main ways to socket white items: the Horodric cube, and Larzuk's quest reward.

You cannot add sockets to or remove sockets from an item that already has sockets, but you can add sockets to unsocketed items. Note that in your case, only the white quality above matters as you can only put Runewords in white items.

Most colored items only give 1 socket, although blue (magic) items will randomly give 1 or 2 sockets. If you add sockets to a colored item this way, you will get fewer sockets. The number of sockets added is based on the specific item you're adding sockets to (it will always get the maximum for an item of that type). You can give white items to Larzuk in Act 5 once per difficulty as a quest reward in order to have him add sockets to the item. An item with sockets has exactly that many sockets forever, and it cannot be altered.
