A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by very (...) simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them. (shrink)