Does recasting Omnath, Locus of creation, reset it's "Landfall Counter?"
Yes. Comprehensive rules 400.7:

An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence.

Followed by some exceptions, none of which apply here. As it's moved from the battlefield to your hand and then back to the battlefield again, it's a new object, so the next land entering the battlefield is the first one it's seen and you gain 4 life.