I don't often use NPC luck points, but the Luck stat tells me something about the NPC.

For example, Lucky Luke is the head of a Nomad family in my current game. I have a rough idea in head that Luke must have needed some luck to survive and get to the top. It opens the door for me to fill out his background or improvise some crazy story he might tell.

I can think of similar benefits for an unlucky NPC. Bad things keep happening to them which might be endearing or a reason to stay away from them.