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@damaggio you can get close to what @adrian_wyer is looking for by using the local settings and adding some divisions to the lattice itself, but there are definitely some artifacts at the borders of cells where the deformation is not smooth. The only way to make it smooth is to bump up the local influence and when you do that the mesh gets too flat.
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You can work around this by having a low-res lattice drive a high-res lattice, an then drive the mesh with the high res lattice. That way even with a high local influence value you still follows the zig-zags. In this particular case though a wire deformer or nonLinear deformer would be simpler.
So I agree with @adrian_wyer there does seem to be an issue with non-continuous deformation between cells.