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In this paper, we introduce the lowering operator (1, c)=(1)-cD(2), where c is an arbitrary complex number and (1) is the generalized Laguerre operator introduced by Dattoli and Ricci. Then, we establish an intertwining relation between the operators (1, c) and the standard derivative D. On the other hand, an analogue of the Hahn characterization of D-classical orthogonal polynomials is given for the operator (1, c). As a consequence, some integral relations between the corresponding polynomials are deduced. Finally, some expansions in series of Laguerre polynomials are studied.