Automorphisms of the category of free Lie algebras

We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism. This solves Problem 3.9 from [G. Mashevitzky, B. Plotkin, E. Plotkin, Electron. Res. Announc. Amer. Math. Soc. 8 (2002) 1–10] for Lie algebras.