In terms of fuzzy soft sets, the notions and fuzzy soft homomorphism of fuzzy soft Lie subalgebras in Lie algebras are defined, and some properties, such as union, intersection and AND, are studied and the following conclusions are proved. If L is a Lie algebra over a field F, (f,A) and (g,B) are fuzzy soft Lie subalgebras on L,then (f,A)∩(g,B) and (f,A)∧(g,B) are still fuzzy soft Lie subalgebras on L,but (f,A)∪(g,B) need not to be fuzzy soft Lie subalgebra on L;if (f,A)k is a family of pre-fuzzy soft Lie ideals on L,then ∪k∈K(f,A)k and ∩k∈K(f,A)k are still pre-fuzzy soft Lie ideals on L.A theorem on fuzzy soft homomorphic pre-image of fuzzy soft Lie subalgebra is proved and a counterexample is given in order to show the image of a fuzzy soft Lie subalgebra under a homomorphism of fuzzy soft Lie subalgebra need not to be a fuzzy soft Lie subalgebra.