A well-known and still open problem for varieties of Lie algebras over zero characteristic field is whether any variety which does not contain a three-dimensional simple algebra is solvable? A. Vais has given a positive answer in the case of special varieties. Here the author shows that the answer is ‘yes’ in the case of varieties with a distributive lattice of subvarieties or when the varieties satisfy the identities of the Witt algebra \(W_ 1\).