Canonically Lazard-dividable Lie ring

Definition
A Lie ring is termed a canonically Lazard-dividable Lie ring if there exists a Lazard-divided Lie ring structure with the Lie ring as underlying Lie ring, such that all the Lazard division operations are invariant under all automorphisms of the Lie ring.

The corresponding Lazard-divided Lie ring is termed a canonically Lazard-divided Lie ring.