We investigate lepton-pair production in hard exclusive hadron-hadron collisions. We consider a double handbag (DH) mechanism in which the process amplitude factorizes in hard subprocesses, qq -> qq gamma* and qg -> qg gamma*, and in soft hadron matrix elements parameterized as generalized parton distributions (GPDs). Employing GPDs extracted from exclusive meson electroproduction, we present predictions for the lepton-pair cross section at kinematics typical for the LHC, NICA and FAIR. It turns out from our numerical studies that the quark-gluon subprocess dominates by far, the quark-quark (antiquark) subprocesses are almost negligible.