Sharma (Appl. Math. Comput. 259:741-752) introduced the mixed summation integral-type two-dimensional q-Lupas-Phillips-Bernstein operators (D) over tilde)(n,m)(qn,qm), wherein he established the rate of approximation by applying Korovkin theorem and studied the weighted approximation properties. The goal of this paper is to establish a Voronovskaja-type theorem and introduce the associated generalized Boolean Sum (GBS) case (T) over tilde)(n,m)(qn,qm) of these operators and study the degree of approximation by the Lipschitz class of Bogel continuous functions and the mixed modulus of smoothness. Furthermore, we show the rate of convergence of the bivariate operators (D) over tilde)(n,m)(qn,qm) and the corresponding GBS operators (T) over tilde)(n,m)(qn,qm) by illustrative graphics and numerical examples using Maple algorithms.