Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras

We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry g∈ O(L) such that gⁱ is fixed point free on L for any 1≤ i≤ |g|-1. We show that when L₂=∅ and gⁱ is fixed point free on L for any 1≤ i≤ |g|-1, VLĝ has extra automorphisms implies either (1) the order of g is a prime or (2) L is isometric to the Leech lattice or some coinvariant sublattices of the Leech lattice.