  Suppose that a Lie type algebra L over a field K admits a Frobenius group of
automorphisms FH with cyclic kernel F of order n and complement H such that the
fixed-point subalgebra of F is trivial and the fixed-point subalgebra of H is
nilpotent of class c. If the ground field K contains a primitive n-th root of
unity, then L is nilpotent and the nilpotency class of L is bounded in terms of
|H| and c. The result extends the known theorem of Khukhro, Makarenko and
Shumyatsky on Lie algebras with metacyclic Frobenius group of automorphisms.
