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Anharmonic crystal lattice dynamics have been observed in lead halide perovskites on picosecond timescales. Here, we report that the soft nature of the perovskite crystal lattice gives rise to dynamic fluctuations in the electronic properties of excited states. We use linear polarization selective transient absorption spectroscopy to study the charge carrier relaxation dynamics in lead-halide perovskite films and nanocrystals. We find that photo-excited charge carriers maintain an initial polarization anisotropy for several picoseconds, independent of crystallite size and composition, and well beyond the reported timescales of carrier scattering. First-principles calculations find intrinsic anisotropies in the transition dipole moment, which depend on the orientation of light polarization and the polar distortion of the local crystal lattice. Lattice dynamics are imprinted in the optical transitions and anisotropies arise on the time-scales of structural motion. The strong coupling between electronic states and structural dynamics requires a unique interpretation of recombination and transport mechanisms.