The free Lie algebra $L(V)$ generated by an $r$-dimensional vector space $V$ is, in the
language of https://en.wikipedia.org/wiki/Free_Lie_algebra ,
the free Lie algebra generated by any choice of basis $e_1, \ldots , e_r$ for the vector space $V$. (Work over the field ${\mathbb R}$ or ${\mathbb C}$, whichever you prefer.)
It is a graded Lie algebra

$$L(V) = V \oplus L_2 (V) \oplus L_3 (V) \oplus \ldots .$$
The general linear group $Gl(V)$ of $V$ acts on $L(V)$ by gradation-preserving Lie algebra automorphisms.
Thus each graded piece $L_k (V)$ is a finite dimensional
representation space for $GL(V)$. (The `weight' of $L_k (V)$ is $k$ in the sense that $\lambda Id \in Gl(V)$ acts on $L_k (V)$ by scalar multiplication by $\lambda^k$.)
QUESTION: How does $L_k (V)$ break up into $GL(V)$-irreducibles?

I only really know that $L_2 (V) = \Lambda ^2 (V)$, which is already irreducible.

To start the game off, perhaps some reader out there already is friends with $L_3 (V)$ as a $GL(V)$-rep, and can tell me its irreps in terms of the Young diagrams / Schur theory involving 3 symbols?

(My motivation arises from trying to understand some details of the subRiemannian geometry http://en.wikipedia.org/wiki/Sub-Riemannian_manifold of the Carnot group whose Lie algebra is the free k-step Lie algebra, which is $L(V)$-trunated after step $k$. )