  We compute the local pro-isomorphic zeta functions at all but finitely many
primes for a certain family of class-two-nilpotent Lie lattices of even rank,
parametrized by irreducible non-linear polynomials $f(x) \in \mathbb{Z} [x]$,
that corresponds to a family of groups introduced by Grunewald and Segal. The
result is expressed in terms of a combinatorially defined family of rational
functions satisfying a functional equation upon inversion of the variables.
