In this paper, we construct free Lie Rota-Baxter superalgebra by using Gr\"{ o}bner-Shirshov bases theory. We firstly construct free operated Lie superalgebras by the operated super-Lyndon-Shirshov monomials. Secondly, we establish Gr\"{ o}bner-Shirshov bases theory for operated Lie superalgebras. Thirdly, we find a Gr\"{ o}bner-Shirshov basis of a free Lie Rota-Baxter superalgebra on a $\mathbb{ Z}_2$-graded set. Consequently, we can obtain a linear basis of a free Lie Rota-Baxter superalgebra by the composition-diamond lemma for operated Lie superalgebras.
Categories: math.RA