$2$-local automorphisms on finite-dimensional Lie algebras
  We prove that every $2$-local automorphism on a finite-dimensional semi-simple Lie algebra $\mathcal{L}$ over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie algebra $\mathcal{L}$ with $\dim \mathcal{L}\geq 2$ admits a $2$-local automorphism which is not an automorphism. 
Shavkat Ayupov, Karimbergen Kudaybergenov
math.RA math.OA