  The aim of this paper is to consider the relation between Lie-isoclinism and
isomorphism of two pairs of Leibniz algebras. We show that, unlike the absolute
case for finite dimensional Lie algebras, these concepts are not identical,
even if the pairs of Leibniz algebras are Lie-stem. Moreover, throughout the
paper we provide some conditions under which Lie-isoclinism and isomorphism of
Lie-stem Leibniz algebras are equal. In order to get this equality, the concept
of factor set is studied as well.
