Automorphism subgroups of the free lie algebra of rank 3

Let $F_r$ be a free Lie algebra over the field $\mathbb C$. We give an example of some subgroup of $\mathrm{Aut}F_r$ that is isomorphic to a subgroup of $\mathbb C^*$ but not conjugated with a subgroup of the linear automorphism group. Some questions are formulated.