Here's what I think I've discoverd. If the object your deforming with the lattice is itself in object mode, then when you group select lattice points and those points sit over the body of the object, it won't work correctly.
If the object is instead set to face (non-object mode), then you are able to group select lattice points and they transform and deform the object as expected.

It's easier to show it than to say it, I'll test this method on an earlier version of my model now to see if this will work in practice.