  We prove sharp upper and lower bounds for generalized Calder\'on's sums
associated to frames on LCA groups generated by affine actions of cocompact
subgroup translations and general measurable families of automorphisms. The
proof makes use of techniques of analysis on metric spaces, and relies on a
counting estimate of lattice points inside metric balls. We will deduce as
special cases Calder\'on-type inequalities for families of expanding
automorphisms as well as for LCA-Gabor systems.
