Is there an example of a $n$ dimensional manifold $M$ and a natural number $k<n$ with a Lie subalgebra $L$ of $\chi^{\infty}(M)$ with the following property:

For every $x\in M$ the space $\{V_x \in T_x M\mid V\in L\} $ is a $k$ dimensional vector space $D_x$ but the distribution $D$ consisting of all $D_x,\;x\in M$ is not an integrable distribution.

In the other word we search for a non integrable distribution $D$ of a manifold and a Lie algebra $L$ of vector fields such that $L$ is $D$-ample where $D$- ample means that the evaluation $L_x$ of $L$ at every point $x$ is equal to $D_x$.