Employing X-ray photon correlation spectroscopy, we measure the kinetics and dynamics of a pressure-induced liquid-liquid phase separation (LLPS) in a water-lysozyme solution. Scattering invariants and kinetic information provide evidence that the system reaches the phase boundary upon pressure-induced LLPS with no sign of arrest. The coarsening slows down with increasing quench depths. The g2 functions display a two-step decay with a gradually increasing nonergodicity parameter typical for gelation. We observe fast superdiffusive (γ ≥ 3/2) and slow subdiffusive (γ < 0.6) motion associated with fast viscoelastic fluctuations of the network and a slow viscous coarsening process, respectively. The dynamics age linearly with time τ ∝ tw, and we observe the onset of viscoelastic relaxation for deeper quenches. Our results suggest that the protein solution gels upon reaching the phase boundary.