Transition-metal-doped perovskite oxide LaNi0.9M0.1O3 (M = Cu, Co) nanosheets were grown on nickel foam to serve as a complete carbon- and binder-free three-dimensional (3D) porous air electrode for lithium–oxygen batteries. The design of this porous air electrode can facilitate rapid gas and electrolyte diffusion, as well as form a continuous electronic conductive network throughout the whole energy conversion process. Because of a combination of abundant lattice strain and the oxygen vacancy effect caused by substitution of an element with a different valence state in Ni sites, LaNi0.9Cu0.1O3 exhibits a significant oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), showing improvement in both aqueous and non-aqueous systems compared with pure LaNiO3 and LaNi0.9Co0.1O3. Especially with the redox mediator additive tetrathiafulvalene (TTF) in the electrolyte, this LaNi0.9Cu0.1O3 perovskite oxide nanosheet catalyst grown on 3D microporous nickel foam exhibits excellent bifunctional catalytic activities in the lithium–oxygen battery, showing the same highly active catalytic kinetics and high round-trip efficiency as those of reported precious metal catalysts. The overpotential remains at 0.72 V, and the round-trip efficiency is up to 80% under a current density of 0.1 mA cm−2, with capacity limited to 1000 mA h g−1.