In this paper, we firstly construct free Lie $Omega$-superalgebras by the super-Lyndon-Shirshov $Omega$-monomials. Secondly, we establish Gr{o}bner-Shirshov bases theory for Lie $Omega$-superalgebras. Thirdly, as an application, we give a linear basis of a free Lie Rota-Baxter superalgebra on a $mathbb{Z}_2$-graded set.
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