Neither the gear type nor the duplex plunger type EW oil pumps return oil to the oil tank, both are total loss systems.
The discussion Ian mentions is
here And a technical article with pictures on the duplex system is
here; only a brief mention is made of the gear type pump.
All I can say about the earlier gear type is that Douglas thought so highly of it they discarded it! I think the main problem was the gear pump had to suck oil from the oil tank compartment at the front of the petrol tank, through a mesh strainer, up through the needle restricing valve and through the drip sight glass on top of the petrol tank, from which point could run by gravity down to the oil pump. The front cylinder non-return valve also provided some suction to the line running to the pump (the line bifurcates just before the oil pump.) Any air leaks in the system would destroy the vacuum, impairing the ability to lift oil through the sight glass. So not only does this early system need to be oil tight, it has to be air tight as well. The non-return valve feeds oil into the front cylinder as stated. The oil pump delivers to the end of the crankshaft, then via drillings to the crankpins. A stand pipe in the bottom of the timing chest leads excess oil off to the primary chain. The level in the timing chest is sufficient to submerge the teeth of the lower cam gear. Additionally, the cam spindles are hollow, and receive vapor from the crank case to lubricate the cam bushes. The hand pump was independent and for use when the mechanical pump failed, not to supplement it. It required turning a petcock through 90 degrees to enable it to supply oil to the sightglass.
An illustration of the early and late oil pump circuit appears in the reprints of "Care and Maintenance of the 350cc E.W. Douglas" available from John Withers
here.-Doug