not sure my frend, i make these suggestions in hope the bigger guns will correct me and in that way help you. from what i remember you can parent the lattice to the grouped geomety so as the gometry moves through it, it deforms. nothing to do with animatng the lattice.
check your help files for a workflow you need??
If you can find a tut from alias' learning tools called, 'hyper real face modelling,' (something like that) it will answer your question, but not in enough time if you are in a hurry.
its just that i remember a work flow similar to this on that tut.
take it easy and life will be easy