Noncommutative Lie algebraic structures on the full vector shift

Let $X = K^\mathbb{Z}$ be the full vector shift, where $K$ is a finite field regarded as a vector space over itself. A nontrivial Lie algebraic subshift structure means a Lie algebraic subshift structure whose bracket is noncommutative.

Full-shift noncommutativity conjecture. The full vector shift $X$ is not compatible with a nontrivial Lie algebraic subshift structure.

This is the first of three classification problems posed for Lie algebraic subshifts, concerning which full vector shifts admit compatible Lie algebraic structures. The source leaves the problem open.