The lighting pied is Marcus Jayne line of Axanthic Pied so in theory only Axanthic Pied using his line of Axanthic should really be called Lighting Pied, but we all know that it is not the case.
The bottom line is that an Axanthic Pied is an Axanthic Pied regardless of the line, also not all equal when it comes to looks since some Axanthic lines look better than others.
None of the Axanthic lines are compatible so if you want to produce Axanthic Pieds you need to pick a line of Axanthic and stick with it, the best looking one and most popular is VPI..