A recent experiment reported the first rare-earth binary oxide superconductor LaO (Tc ∼ 5 K) with a rock-salt structure [K. Kaminaga et al., J. Am. Chem. Soc. 140, 6754 (2018)]. Correspondingly, the underlying superconducting mechanism in LaO needs theoretical elucidation. Based on firstprinciples calculations on the electronic structure, lattice dynamics, and electron-phonon coupling of LaO, we show that the superconducting pairing in LaO belongs to the conventional Bardeen-Cooper-Schrieffer (BCS) type. Remarkably, the electrons and phonons of the heavy La atoms, instead of those of the light O atoms, contribute most to the electron-phonon coupling. We further find that both the biaxial tensile strain and the pure electron doping can enhance the superconducting Tc of LaO. With the synergistic effect of electron doping and tensile strain, the Tc could be even higher, for example, 11.11 K at a doping of 0.2 electrons per formula unit and a tensile strain of 4%. Moreover, our calculations show that the superconductivity in LaO thin film remains down to the trilayer thickness with a Tc of 1.4 K.