  We give a sufficient criterion for generic local functional equations for
submodule zeta functions associated to nilpotent algebras of endomorphisms
defined over number fields. This allows us, in particular, to prove various
conjectures on such functional equations for ideal zeta functions of nilpotent
Lie lattices. Via the Mal'cev correspondence, these results have corollaries
pertaining to zeta functions enumerating normal subgroups of finite index in
finitely generated nilpotent groups, most notably finitely generated free
nilpotent groups of any given class.
