“na'e” means “other than” and not “not”. Thus, “c1 does not
eat meat c2=r1” is nonsense. It even contradicts with “c1 is a
lacto-ovo-vegetarian”. Both sentences are not equivalent, because the
first sentence makes no assertions about wheather or not milk eggs and
milk are consumed.
Also the meat sumti is clearly not relevant to the definition, since a
lacto-ovo-vegetarian does, by definition, not eat any meat whatsoever.
I wrote another definition getting rid of the first sentence.