  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.
