Lead halide perovskites are strong candidates for high-performance low-cost photovoltaics, light emission, and detection applications. A hot-phonon bottleneck effect significantly extends the cooling time of hot charge carriers, which thermalize through carrier-optic phonon scattering, followed by optic phonon decay to acoustic phonons and finally thermal conduction. To understand these processes, we adjust the lattice dynamics independently of electronics by changing isotopes. We show that doubling the mass of hydrogen in methylammonium lead iodide by replacing protons with deuterons causes a large 20 to 50% softening of the longitudinal acoustic phonons near zone boundaries, reduces thermal conductivity by ~50%, and slows carrier relaxation kinetics. Phonon softening is attributed to anticrossing with the slowed libration modes of the deuterated molecules and the reduced thermal conductivity to lowered phonon velocities. Our results reveal how tuning the organic molecule dynamics enables control of phonons important to thermal conductivity and the hot-phonon bottleneck.