Ok, in that section, he's applying a lattice there because he's using a multi-patch nurbs model. If you're not using Nurbs, I wouldn't worry about doing that.

The lattice in question is just a simple lattice. You should have an easy enough time of creating an identical one on the other side. He doesn't actually use the lattice for animating. He uses it to keep the multi-patch together when bending the thumb joint, but he still animates using bones like normal.

This can also be done with flexors when rigid binding. A flexor is essentially, a lattice.