Throughout we shall consider only finite-dimensional Lie algebras over a field of characteristic zero. In  it was shown that the classes of solvable and of supersolvable Lie algebras of dimension greater than two are characterised by the structure of their subalgebra lattices. The same is true of the classes of simple and of semisimple Lie algebras of dimension greater than three. However, it is not true of the class of nilpotent Lie algebras. We seek here the smallest class containing all nilpotent Lie algebras which is so characterised.
http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 29 (1), pp 7-11 1987, © 1987 Cambridge University Press.