  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.
