The Lennox is unusual for an Australian-made bike as it uses a locally-made engine, with a cylinder and head based on John Duigan's aeroplane - the first Australian built plane to fly. The first four bikes - single speeders - used the actual cylinders and heads off the first iteration of the aeroplane engine, which flew but had only just enough power and tended to overheat. The cylinders and head of this engine were replaced by the manufacturer, J. E. Tilley & Co. in Melbourne, with larger bore cylinders and water cooled heads, and the originals were used by Tilley employee Robbie Robertson, and later his friend Bob King, to build four motor cycles. Subsequent bikes, like mine, used cast copies of the cylinders (originals were machined from steel) and newly-cast heads. According to Robbie Robertson, my bike was the only Lennox fitted with a gearbox (4 speed Jardine). In 1915, while on leave from the Navy, Robbie rode the bike from Bob King's Lennox St motor works down to Yeats' sidecar works further along the street to have the sidecar fitted. So, yes, the whole story is known, much of it from the mouths of those who built it since the previous owner had the bike from 1955 until recently.
Leon