No, it's not an "Australian copy of FEB Bakers Precision Motor" but a motor built by F.E. Baker for Lewis. The motors were not branded Precision (they usually has Lewis cast into the crankcase, and were usually stamped "Made in England" - a posible clue), and the cylinders (even the air cooled ones) were different from those used by Precision: presumably this was a way of Lewis getting around the fact the A.G. Healing in Melbourne were the Australia-wide agents for Precision engines. The Lewis motors were shipped directly to Lewis in Adelaide.
Nice bike.
Leon
Edit: Should have added: the cycle parts (lugs, wheel hubs, forks, pedalling gear, brakes...) are British Chater Lea. Frames were brazed up and enameled at Lewis; plating was also done in house. The tanks were made my a local Adelaide tinsmith called Memmler. On this model, the whole affair where the tank usually goes comprises a water tank and radiator at the front, and the fuel tank is beneath the saddle. This necessitated a British B&B carb with a really long body to get the float bowl low enough so that the fuel could run into it. I've not seen this carb elsewhere, so like the engine it might have been a special build for Lewis.