Geodesic
On varieties of Lie algebras not containing a~three-dimensional simple algebra
Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 189-197

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It is proved that in the case of zero characteristic of the ground field a variety of Lie algebras not containing a 3-dimensional simple algebra is solvable in the following cases: 1) The variety has a distributive lattice of subvarieties. 2) The variety satisfies all the identities of the infinite-dimensional Witt algebra. 
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     author = {S. P. Mishchenko},
     title = {On varieties of {Lie} algebras not containing a~three-dimensional simple algebra},
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S. P. Mishchenko. On varieties of Lie algebras not containing a~three-dimensional simple algebra. Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 189-197. http://geodesic.mathdoc.fr/item/SM_1993_76_1_a9/