Let A be a unital algebra with a nontrivial idempotent e, and f = 1 − e. Suppose that A satisfies that exe · eAf = {0} = fAe · exe implies exe = 0, and that eAf · f x f = {0} = f x f · fAe implies f x f = 0 for each x in A. For a Lie n-derivation ϕ on A, we obtain the necessary and sufficient conditions for ϕ to be standard, i.e., ϕ = d + γ, where d is a derivation on A, and γ is a linear mapping from A into the centre Z(A) vanishing on all (n − 1)−th commutators of A. Furthermore, we also consider the sufficient conditions under which each Lie n-derivation on A can be standard.