Hello Ted, I think that the engine number you have quoted is missing a digit. Not many LFZ/LFY engines were made, and my 1934 has engine number LFZ 3996, so the one you mention should be VERY close to that. The engine should be a detachable cylinder head long-stroke. Ian Parsons should have more information.
This bike does not appear on the Machine Register. Every year 2 or 3 “unknown” Scotts reappear and of course are very welcome. Equally many Scotts well known 20-30years ago have gone missing, mainly because previous owners have died or left the Club. Theoretically there are plenty of Scotts to go round but unfortunately most are hidden away.
I did say that it would be VERY close to my LFZ 3996, and it turns out that it is LFY 3992 ! I can just imagine those men at Shipley 79 years ago, finishing them off, probably within a few days of each other, maybe even on the same day…. but in reality I think that it would only have been the engines that were born in the same litter, with the bikes being made one at a time to meet the poor demand of 1934.