  Three $q$-versions of Lommel polynomials are studied. Included are explicit
representations, recurrences, continued fractions, and connections to
associated Askey--Wilson polynomials. Combinatorial results are emphasized,
including a general theorem when $R_I$ moments coincide with orthogonal
polynomial moments. The combinatorial results use weighted Motzkin paths,
Schr\"oder paths, and parallelogram polyominoes.
