Applying time differential perturbed angular correlation (TDPAC) spectroscopy and emph{ab initio} calculations, we have investigated possible lattice instabilities in Sr$_{2}$RuO$_{4}$ by studying the electric quadrupole interaction of a $^{111}$Cd probe at the Ru site. We find evidence for a dynamic lattice distortion, revealed from the observations of: (i) a rapidly fluctuating electric-field gradient (EFG) tensor of which the main component decreases with decreasing temperature, and (ii) a monotonic increase of the EFG asymmetry ($eta$) below 300 K. We argue that the observed dynamic lattice distortion is caused by strong spin fluctuations associated with the inherent magnetic instability of Sr$_{2}$RuO$_{4}$.
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