Recently, the discovery of room-temperature superconductivity (SC) was experimentally realized in the fcc phase of LaH$_{10}$ under megabar pressure. Specifically, the isotope effect of $T_{rm c}$ was measured by the replacement of hydrogen (H) with deuterium (D), demonstrating a driving role of phonons in the observed room-temperature SC. Herein, based on the first-principles calculations within the harmonic approximation, we reveal that (i) the identical electron-phonon coupling constants of fcc LaH$_{10}$ and LaD$_{10}$ decrease monotonously with increasing pressure and (ii) the isotope effect of $T_{rm c}$ is nearly proportional to $M^{-{alpha}}$ ($M$: ionic mass) with ${alpha}$ ${approx}$ 0.465, irrespective of pressure. The predicted value of ${alpha}$ agrees well with the experimental one (${alpha}=0.46$) measured at around 150 GPa. Thus, our findings provide a theoretical confirmation of the conventional electron-phonon coupling mechanism in a newly discovered room-temperature superconductor of compressed LaH$_{10}$.
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