We discuss heavy-lepton pair production via the reaction $\ensuremath{\gamma}+Z\ensuremath{\rightarrow}{L}^{+}+{L}^{\ensuremath{-}}+Z$ followed by the decays ${L}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}+\ensuremath{\nu}+\overline{\ensuremath{\nu}}$ or ${L}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{e}^{\ifmmode\pm\else\textpm\fi{}}+\ensuremath{\nu}+\overline{\ensuremath{\nu}}$. Particular attention is given to the energy and angular distributions of the final detected leptons. The only reasonable signal for heavy-lepton production seems to be the detection of $\ensuremath{\mu}e$ pairs in relatively quiet events. In the case of $\ensuremath{\mu}\ensuremath{\mu}$ pairs the signal from the decay of the heavy-lepton pairs is much smaller than the background due to regular Bethe-Heitler production for both the cross section and for all the differential spectra.