Old post I know, but my answer is relevant. I found this thread when researching a replacement (lost) rad cap for my 3940.
Radiator caps and filler necks are manufactured to SAE J164 standard (actually a "recommended practice"). With a little digging I discovered that my rad cap is a "mini", and by confirming a few dimensions on my radiator fill neck (internal diameter, depth to seal surface, outside diameter and then selecting the pressure rating - I was able to identify a replacement as Gates 31333.
LS (or any tractor manufacture) does not make their own rad caps, nor most "consumable" components, so I just takes a little homework to find a compatible part.