If $A$ is an arbitrary algebra over a field of characteristic $p>0$, then its derivation algebra is a restricted Lie algebra under the usual Lie bracket $[D_1,D_2]=D_1D_2-D_2D_1$ and the ordinary $p$-exponentation. This show that, in positive characteristic, a non-restrictable Lie algebra cannot be the derivation algebra of an algebra of any kind.

If $A$ is an arbitrary algebra over a field of characteristic $p>0$, then its derivation algebra is a restricted Lie algebra under the usual Lie bracket $[D_1,D_2]=D_1D_2-D_2D_1$ and the ordinary $p$-exponentation. This shows that, in positive characteristic, a non-restrictable Lie algebra cannot be the derivation algebra of an algebra of any kind.