First I've heard of Greener building Lee-Enfields for the Great War. BSA, LSA, Sparbrook, and Enfield Arsenal were the main, if not only, ones (aside from the production taking place out in the colonies). I would expect Greener to have built sporting rifles on the L-E. It seems a lot of the big purveyors of such arms did that. If I'm wrong, I will stand corrected.
There followed 20 years later, some "schemes" to build Enfields by the process of farming out all of the bits and pieces to subcontractors which were then assembled by third parties.