  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.
