  We develop a version of the Bass-Serre theory for Lie algebras (over a field
$k$) via a homological approach. We define the notion of fundamental Lie
algebra of a graph of Lie algebras and show that this construction yields
Mayer-Vietoris sequences. We extend some well known results in group theory to
$\mathbb{N}$-graded Lie algebras: for example, we show that one relator
$\mathbb{N}$-graded Lie algebras are iterated HNN extensions with free bases
which can be used for cohomology computations and apply the Mayer-Vietoris
sequence to give some results about coherence of Lie algebras.
