  In this paper, we introduce the notion of Rota-Baxter Lie $2$-algebras, which
is a categorification of Rota-Baxter Lie algebras. We prove that the category
of Rota-Baxter Lie $2$-algebras and the category of $2$-term Rota-Baxter
$L_\infty$-algebras are equivalent. We introduce the notion of a crossed module
of Rota-Baxter Lie algebras and show that there is a one-to-one correspondence
between strict $2$-term Rota-Baxter $L_\infty$-algebras and crossed modules of
Rota-Baxter Lie algebras. We give the construction of crossed modules of Lie
algebras from crossed modules of Rota-Baxter Lie algebras.
