A recent experiment reported the first rare-earth binary oxide superconductor LaO ($T_c $ $sim$ 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 first-principles 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 $T_c$ of LaO. With the synergistic effect of electron doping and tensile strain, the $T_c$ 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 $T_c$ of 1.4 K.
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