Hi Sludgetrap,
I believe the L2/1 was a lightweight version of the 2/1. Looking at the specs from the 1935 range, it seems that the L2/1 had a smaller gas tank (2.25 vs 2.75 gals), smaller oil tank (3.5 vs 4 pints), 6" brakes instead of 7" and a pressed steel primary case instead of the aluminium oil bath which the 2/1 had.
Is the bike in your display pic the one in question? If I recall correctly, wasn't it up on ebay Australia recently?
Hope this helps