Let $\Pi=(P,L)$ be a partial linear space in which any line contains three
points and let $K$ be a field.
Then by ${\cal L}_K(\Pi)$ we denote the free $K$-algebra generated by the
elements
of $P$ and subject to the relations $xy=0$ if $x$ and $y$ are noncollinear
elements from $P$ and $xy=z$ for any triple $\{x,y,z\}\in L$.
We prove that the algebra ${\cal L}_K(\Pi)$ is a Lie algebra if and only if $K$ is of even
characteristic and $\Pi$ is a cotriangular space satisfying Pasch's axiom.
Moreover, if $\Pi$ is a cotriangular space satisfying Pasch's axiom,
then a connection between derivations of the Lie algebra ${\cal L}_K(\Pi)$
and geometric hyperplanes of $\Pi$ is used to determine the structure of the
algebra of derivations of ${\cal L}_K(\Pi)$.