Two types of pseudoscalar quarkonium electromagnetic decay processes, i.e. decay to a lepton pair, and to a lepton pair plus a photon (Dalitz decay), are analyzed at the leading order in NRQCD expansion. The former type of processes, highly suppressed in the Standard Model, have been hoped to act as the sensitive probes of the possible new physics. The latter type of processes generally possess much greater decay rates than the former, owing to several conspiring factors. The recently launched BES-III program, with 10⁸ η_c samples to be anticipated in the coming years, may be able to observe the Dalitz decays η_c → e⁺e⁻γ and η_c → μ⁺μ⁻γ, which have branching ratios of order 10⁻⁶. When the radiated photon becomes very soft, the Dalitz decay events will be experimentally tagged as the exclusive lepton pair events. It is found that, those quasi-two-body events that arise from η_c → e⁺e⁻γ with photon energy less than the minimum sensitivity of the electromagnetic calorimeter, can vastly outnumber the literal η_c → e⁺e⁻ events, however this amplification is still not dramatic enough for the BES-III experiment to establish these events. Consequently, the expectation of looking for new physics signature in the η_c → l⁺l⁻ channel is obscured, unless the contamination from η_c → l⁺l⁻γ has been taken into account carefully.