  We prove the existence of a model companion of the two-sorted theory of
$c$-nilpotent Lie algebras over a field satisfying a given theory of fields. We
describe a language in which it admits relative quantifier elimination up to
the field sort. Using a new criterion which does not rely on a stationary
independence relation, we prove that if the field is NSOP$_1$, then the model
companion is NSOP$_4$. We also prove that if the field is algebraically closed,
then the model companion is $c$-NIP.
