The development of X-ray free-electron lasers (XFELs) has opened the possibility to investigate the ultrafast dynamics of biomacromolecules using X-ray diffraction. Whereas an increasing number of structures solved by means of serial femtosecond crystallography at XFELs is available, the effect of radiation damage on protein crystals during ultrafast exposures has remained an open question. We used a split-and-delay line based on diffractive X-ray optics at the Linac Coherent Light Source XFEL to investigate the time dependence of X-ray radiation damage to lysozyme crystals. For these tests, crystals were delivered to the X-ray beam using a fixed-target approach. The presented experiments provide probe signals at eight different delay times between 19 and 213 femtoseconds after a single pump event, thereby covering the time-scales relevant for femtosecond serial crystallography. Even though significant impact on the crystals was observed at long time scales after exposure with a single X-ray pulse, the collected diffraction data did not show significant signal reduction that could be assigned to beam damage on the crystals in the sampled time window and resolution range. This observation is in agreement with estimations of the applied radiation dose, which in our experiment was clearly below the values expected to cause damage on the femtosecond time scale. The experiments presented here demonstrate the feasibility of time-resolved pump-multiprobe X-ray diffraction experiments on protein crystals.