Lazurk will add the max amount sockets to an item based the ilvl of the item, i.e : if you get a crystal sword from normal cows it will socket to 4os, however if you get one from nightmare act 1 onwards it will socket to 5 and so-forth,
it all depends on the ilvl of the item (where it is dropped).
Since Dusk Shrouds are an elite base and are at least ilvl 65, Lazurk socketing them will always provide 4 sockets.
As for cube socketing, if you socket a normal quality Dusk Shroud you have a 1/6 chance (roughly 16%) to get either 1, 2 or 3 sockets and a 3/6 50% chance to get 4 sockets, keep in mind you cannot cube socket superior items but.
Hopefully that answers all your questions!