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We investigate the transient photoexcited lattice dynamics in a layered perovskite Mott insulator Sr2IrO4 by femtosecond X-ray diffraction using a laser plasma-based X-ray source. Ultrafast structural dynamics of Sr2IrO4 thin films are determined by observing the shift and broadening of the (0012) Bragg diffraction after excitation by 1.5 eV and 3.0 eV pump photons for films with different thicknesses. The observed transient lattice response can be well interpreted as a distinct three-step dynamics due to the propagation of coherent acoustic phonons generated by the photoinduced quasiparticles (QP). Employing a normalized phonon propagation model, we found that the photoinduced angular shifts of the Bragg peak collapse into a universal curve after introducing a normalized coordinates to account for different thicknesses and pump photon energies, pinpointing the origin of the lattice distortion and its early evolution. In addition, a transient photocurrent measurement indicates that the photoinduced QPs are charge neutral excitons. Mapping the phonon propagation and correlating its dynamics with the QP by ultrafast X-ray diffraction (UXRD) establish a powerful way to study electron-phonon coupling and uncover the exotic physics in strongly correlated systems under nonequilibrium conditions., Comment: 11 pages,4 figures