When the equipped creature becomes the target of a spell, the ability granted to it by Livewire Lash will trigger and go on the stack on top of it. It will resolve before the spell does.

The equipped creature is the source of both the triggered ability and the resultant damage, not Livewire Lash. For example, you can target and deal damage to a creature with protection from artifacts (assuming the equipped creature isn't an artifact itself, of course).