We develop the full finite lepton mass formalism for the Bethe-Heitler reaction of unpolarized leptons off unpolarized nucleons. Genuine lepton mass effects are described, notably independent of the lepton mass or increasing with the initial beam energy and sensitive to the nucleon isospin. In the minimum momentum transfer region, these effects dominate the muon induced proton cross section and become significant for electron scattering at small $x_B$.