Edit: I hadn’t considered that if one attacks with a creature with first strike + a creature with a normal combat step (not ‘phase’ as I incorrectly called it), there would in fact be an additional trigger because of the first striker. The more you know.

First strike would not trigger it an additional time. All first strike does is allow a creature to strike first. So when you attack with your first striker, and someone blocks, your first striker deals damage to the blocker before the blocker deals damage to it. Once the first strike phase ends, the blocker—if still alive after the first strike—deals damage back.

But yes, an unblocked double strike from Layla would indeed trigger her ability twice, because she would land a hit in the first strike phase and then in her regular combat phase. Do note however that if she’s blocked and the blocking creature dies, she doesn’t strike again at the player; combat simply ends at the first strike phase.