There is a large literature on cohomology of Lie algebras. Here is a very short list of articles and books:

C. Chevalley, S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124.

G. P. Hochschild, J.-P. Serre, Cohomology of Lie algebras, Ann. of Math. 57 (1953), 591-603.

J. L. Koszul, Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France , 78 (1950) pp. 65–127

J. C. Jantzen, Representations of Algebraic groups, Pure and Applied Mathematics, vol. 131, Boston, etc., 1987 (Academic).

J. C. Jantzen, Restricted Lie algebra cohomology, Lecture Notes in Math. 1271 (1986), 91-108.

A. W. Knapp, Lie groups, Lie algebras and cohomology, Mathematical Notes, Princeton University Press, 1988, 509 pp.

As far as I know, a generalisation of Poincare duality for Lie algebra cohomology over rings is given in

M. Hazewinkel, "A duality theorem for the cohomology of Lie algebras" Math. USSR-Sb. , 12 (1970) pp. 638–644.

There is a large literature on cohomology of Lie algebras. Here is a very short list of articles and books:

C. Chevalley, S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124.

G. P. Hochschild, J.-P. Serre, Cohomology of Lie algebras, Ann. of Math. 57 (1953), 591-603.

J. L. Koszul, Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France , 78 (1950) pp. 65–127

J. C. Jantzen, Representations of Algebraic groups, Pure and Applied Mathematics, vol. 131, Boston, etc., 1987 (Academic).

J. C. Jantzen, Restricted Lie algebra cohomology, Lecture Notes in Math. 1271 (1986), 91-108.

A. W. Knapp, Lie groups, Lie algebras and cohomology, Mathematical Notes, Princeton University Press, 1988, 509 pp.