I'm far from an Apex wizard , but I checked your scene and think I see part of the problem.
The lattice deformer can't handle 2 separate "bound" deformers , it can only handle a single connected bound deformer , like a regular lattice cage.
So when I disable the second bounding box ( after the "bound" SOP ), at least the Left X part of the eye deforms. And when I disable the whole "Foreach" block so only the "bound" SOP is active , it creates a single bound and deforms both X shapes.
I don't know if the circle part of the eyes should be visible or deform as well , but maybe this is a step in the right direction.
But I attached the scene where only a single X deforms.
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