I've never handled a Sig 556 pistol, but I'm thinking if my RLL will work, it'd be a sweet little rig, if I added a folding stock. (while the LL is inserted, of course).
Since I've never handled one I have no idea what the fire control components look like.
The basic answer is no, it won't work. There are a couple reasons for that too. First and foremost is that its not legal. The lightning link is made and registered for use in the AR lowers and I think its limited to the AR15's as well. This means its not legal to use in a weapon other than what its intended for....ie no use in SIG's , FN's etc.
Secondly and also very important, the trigger group in the SIG is completely different than the AR so the link won't fit the lower or the trigger parts. The whole operating system is different.