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We compute the local pro-isomorphic zeta functions at all but finitely manyprimes 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. Theresult is expressed in terms of a combinatorially defined family of rationalfunctions satisfying a functional equation upon inversion of the variables.

Pro-isomorphic zeta functions of some $D^\ast$ Lie lattices of even rank