In this paper we study a certain recurrence relation, that can be used to generate ladder operators for the Laguerre unitary ensemble, from the point of view of Sakai’s geometric theory of Painlev´e equations. On one hand, this gives us one more detailed example of the appearance of discrete Painlev´e equations in the theory of orthogonal polynomials. On the other hand, it serves as a good illustration of the effectiveness of a recently proposed procedure on how to reduce such recurrences to some canonical discrete Painlev´e equations.