 The scenario is under-described. We can imagine that the means of turning the lamp off and on requires a spacetime location at which at least one physical quantity is infinite. If so, it is plausible to say that the case is impossible: there could not be such a lamp, and so there is no question to answer. Suppose, for example, that there is a switch that moves the same distance back and forth to turn the lamp on and off. Consider the speed at which the tip of the switch is travelling at the end of the second minute.