With a spool no special additive is needed... whale oil or otherwise. For your intended use just about any gear lube - like 80W90 - should work OK.

Sustained high speed running and/or high temps would favor higher viscosity synthetic to take the heat but not an issue on the drag strip. xxW-140.

The last .01 second ET in the quarter mile might favor favor a lighter synthetic like 75W90.

Personally I would probably put 80W-90 in it.