<p>A general theory for the exchange timescale of lock-exchange flows where both the lock and the ambient are stratified has not been established yet. Here, two-dimensional large-eddy simulations of the lock exchange are performed, to quantify the dependence of the adjustment time on linear stratification in the lock and ambient. After validation of the model, simulations show that stratification in the ambient decreases the adjustment time, which is related to an increase of the hydrostatic pressure difference driving the front traveling into the lock. Stratification in the lock also decreases the adjustment time, because a larger stratification is associated with faster internal waves, thereby highlighting the role of internal wave speed in the stratified lock exchange. A reduced model for adjustment time is developed, that extends known relations for front speeds in unstratified conditions to situations with a vertically stratified lock and ambient. Stratification is incorporated by combining its effects on hydrostatic pressure and internal wave speed. This reduced model reproduces the dependence of the adjustment time on the initial density field with reasonable accuracy.</p>