The lazy cop number is the minimum number of cops needed for the cops to have a winning strategy in the game of Cops and Robbers where at most one cop may move in any round. This variant of the game of Cops and Robbers, called Lazy Cops and Robbers, was introduced by Offner and Ojakian, who provided bounds for the lazy cop number of the hypercube. In this paper, we are interested in the game of Lazy Cops and Robbers on generalized hypercubes. Generalizing existing methods, we will give asymptotic upper and lower bounds on the lazy cop number of the generalized hypercube.