Sunhome Enforcer does not have likelink! Read the card!
True, Whenever (card name) deals combat damage, you gain that much life != lifelink
Here's a list of cards with this wording and the ability lifelink. It's taken from the SVN rev 2294 so either all this cards get remover or all cards worded like this gets added to the primitives:
Paladin of Prahv
I would hate to see all those cards removed but the rules aren't the same for lifelink and this ability due to the stack o gain life, lifelink doesn't stack, the other one does.
Even a bunch of these cards are in AI decks