  We consider finite-dimensional complex Lie algebras. We generalize the
concept of Lie derivations via certain complex parameters and obtain various
Lie and Jordan operator algebras as well as two one-parametric sets of linear
operators. Using these parametric sets, we introduce complex functions with
fundamental property - invariance under Lie isomorphisms. One of these
basis-independent functions represents a complete set of invariant(s) for
three-dimensional Lie algebras. We present also its application on physically
motivated examples in dimension eight.
