Did this tool come with a 1020? It is usually seen with a 1001/1014/1015. Maybe the early 1020s used it.
From what I can see in the catalogues, this tool was used for the 1020 (and 991) until 1944. In 1945 they are listed as using the tool you show as coming from a 981. Btw, this tool has part number 6333.
A 30's model 1020 with a solid brass knob came with this partly cupped spanner. This odd shape was perhaps thought to help with getting grips while under a steep angle - I 'm only guessing.
It makes sense to only have one tool that works on several lamps. From what I can see, the curve is only needed on the 1001/1014/1015 burner to fit under the air tubes.