  Similar to works of G. Ellis (1998), the concept of covering pair of Lie
algebras is defined. Also, we show the existence of covering pair for the pair
of Lie algebras (L,N) and then show that every crossed module is a homomorphic
image of a covering pair of (L,N). Finally, under some condition, we present
some inequalities for the Schur multiplier of a pair of finite dimensional Lie
algebras.
