Very efficient machinery has been developed for constructing a Gröbner basis for a finitely presented Lie algebra L by Willem de Graaf and Allan Steel. The GB reduction algorithm used is Magma's generic F4 algorithm. At present, if the algebra L is finite dimensional, the GB can be used to construct a Lie algebra defined by structure constants. Alternatively, the GB may be used to construct a nilpotent quotient of L to a designated class.