In a nonequlibrium plasma of a gas-discharge HgBr lamp, the terminal electronic state of the HgBr(B-X) radiative transition with a peak wavelength of 502 nm remains populated for a relatively long time and is repeatedly excited to the B state in collisions with plasma electrons. This transfer of the HgBr molecules from the ground state X to the excited state B is the main mechanism of formation of the light-emitting molecules especially when the lamp is excited by double current pulses. According to our simulations, due to the electron-induced transitions between HgBr(X) and HgBr(B), the output characteristics of the DBD lamp operating in a double-pulse regime are better than those of the lamp operating in a single-pulse regime. In the considered case, the peak power is calculated to increase by a factor of about 2 and the lamp efficiency increases by about 50%.