in the talk we consider lie algebras with one defining relation. starting with an analog of freiheitssatz (shirshov's theorem), we give an example of a lie algebra over a field of prime characteristic with cohomological dimension one which is not a free lie algebra (this gives a counterexample to a hypothesis that the analog of stallings-swan theorem takes place for lie algebras; the problem in the case of field of zero characteristic is still open, we formulate some related conjectures). for a finitely generated free lie algebra l we construct an example of two elements $u$ and $v$ of $l$ such that the factor algebras $l/(u)$ and $l/(v)$ are isomorphic, where $(u)$ and $(v)$ are ideals of l generated by $u$ and $v$, respectively, but there is no automorphism $f$ of $l$ such that $f(u)=v$. we consider also the situation where a lie algebra with one defining relation is a free lie algebra.