There are two issues to consider: the generic locktime of an action and the specific lock time of one particular rifle.
According to the table in Vol.1 of Stuart Otteson's The Bolt Action, the Mosin has a lock time of 5.9 milliseconds, and the MkIII Lee Enfield 7.3 ms. I would assume these are unaltered military actions, in good conditon.
You can take his numbers as the best case. Any individal rifle may function more slowly due to friction from parts fitting, gunk in the bolt or a weak firing pin spring. Never mind the effect of old ammo with primers that could cause imperceptible hangfires.
There are modifications for the Lee Enfield that can improve lock time, since decades of Bisley shooters and gunsmiths have played with this action. Usually improvements feature better triggers, faster springs and low-mass strikers. Don't know whether the same is true for the MN.