Proteases can be either reversible or irreversible.
Reversible proteases react in the absence or above critical concentrations of their inhibitors. Often in the literature, cocktails of inhibitors are made up and little thought goes into what they are effective against, what concentrations are needed, and how long they are stable in an aqueous environment. A case in point is PMSF, a widely used serine protease. So it should be added just before the cell lysis. Still working on aspartic.