You mention that the baby's lips were not originally flanged out.  Are you
sure baby is nursing with flanged lips when you aren't there.  What about
having mom use a hospital grade electric pump with a double set-up and
supplement with pumped milk using a supplemental nurser system?
If that isn't the problem, it seems to me that a second opinion from a
physician or a speech therapist, occupational therapist, or physical
therapist trained in infant feeding disorders would be appropriate.
Eliminating milk seems like a good idea.  If there is a strong family history
of allergies, eliminating other allergenic food might be a good idea, or what
about a consult with a pediatric allergist?  Please let us know how this
comes out.  Bonnie