Purely leptonic bound states provide precision probes of QED. Positronium $(e^{+}{e}^{-})$ and muonium $({\mu }^{+}{e}^{-})$ have long been observed, whereas dimuonium $({\mu }^{+}{\mu }^{-})$ and tauonium $({\tau }^{+}{\tau }^{-})$ remain undiscovered. We study exclusive vector-leptonium electroproduction in $ep$ collisions within nonrelativistic QED. We include the Bethe–Heitler and double deeply virtual Compton scattering contributions and their interference, and calculate the NLO QCD hard-scattering kernels entering the dominant Compton form factor $\mathscr{H}$ within collinear GPD factorization. The NLO QCD correction to the DDVCS contribution changes from a strong suppression at low photon virtuality to a sizable enhancement as the lower virtuality cut is raised, with the gluon channel providing the dominant contribution. The integrated dimuonium rate is dominated by BH, whereas DDVCS can exceed BH at larger skewness, providing a kinematic window for probing proton GPDs. We further evaluate positronium, dimuonium, and tauonium production rates at representative facilities to assess the prospects for leptonium searches and future precision studies of bound-state QED.