Let X be a complex Banach space with dimension greater than 1. Let L be a subspace lattice of X with X − = X or {0} + = {0}. Assume that L : AlgL → AlgL is a linear Lie n-derivation. It is shown that L(A) = δ(A) + f (A) for all A ∈ AlgL, where δ : AlgL → AlgL is a linear derivation and f is a linear functional of AlgL vanishing at every (n − 1)th commutator of AlgL.