Baking lattices to shape keys?

I’m trying to rig a character for exporting to the Unreal 4 engine, and I want to be able to create shape keys using lattices. Basically, I have a bunch of different objects that need to be morphed with lattices in order to make my customization system work. I don’t want to add more bones to the rig and complicate things, what I’d like to do is setup lattices to deform with that I can rig the objects to, and then have the lattice poses converted to shape keys on export. Is there any way to do this? If I create shape keys for the lattice then will all the objects affected by that lattice have shape keys based on the lattice when exported to FBX? Pretty much what I’m going for, is that I’d like to make shape keys with lattices, because if the body mesh is deformed by a shape key (for weight/muscle slider in character creation) I want the clothes to follow along.

Currently I think you will need to manually apply the lattice modifier as a shape key to each mesh, for each shape key of the lattice. This will obviously be fairly tedious if there are a lot of meshes and or shapes.
It would be possible to automate this with python though.