In this paper we present interpretations of Lommel polynomials and their derivatives. A combinatorial interpretation uses matchings in graphs. This gives an interpretation for the derivatives as well. Then Lommel polynomials are considered from the point of view of operator calculus. A step-3 nilpotent Lie algebra and finite-difference operators arise in the analysis.
Feinsilver, Philip J., McSorley, John P. and Schott, René. "A Combinatorial Interpretation of Lommel Polynomials and Their Derivatives." (Jul 1996).