  We give a lattice-theoretic classification of non-symplectic automorphisms of
prime order of irreducible holomorphic symplectic manifolds of OG10 type. We
determine which automorphisms are induced by a non-symplectic automorphism of
prime order of a cubic fourfold on the associated LSV manifolds, giving a
geometric and lattice-theoretic description of the algebraic and transcendental
lattices of the cubic fourfold. As an application we discuss the rationality
conjecture for a general cubic fourfold with a non-symplectic automorphism of
prime order.
