  Very recently, a report on possible room-temperature superconductivity in
N-doped lutetium hydrides near 1 GPa pressure has drawn lots of attentions. To
date, the superconductivity is not confirmed under relatively low pressure in
subsequent studies. Based on the density functional theory first-principles
calculations, we extensively investigate the influence of charge doping on the
stability and superconductivity of LuH$_3$ at ambient pressure. Although
electron doping can not stabilize LuH$_3$, we find that the room-pressure
stability of LuH$_3$ can be achieved by doping holes with concentrations in
between 0.15-0.30 holes/cell. Moreover, our calculations reveal a positive
dependence of superconducting transition temperature on the number of doped
holes, with the highest value close to 54 K. These findings suggest that
realizing superconductivity in hole-doped LuH$_3$ at ambient pressure is not
impossible, although the transition temperature is still far away from the room
temperature.
