i think it might fit, but you won't get much light out of if because the L2's circuit is built in the body itself, that's why its slightly longer than the L4.
If you want a great mod, pull the Lux V out of the L2 head and replace it with a good Lux III. Then put it on your E2e body and power it with a Pila. Really bright with lots of throw.
hmmm, i think the L2 body actually has some circuitry in it to power the L2 head if i remember correctly. I think once i took the head off, and turned it on to see where that high pitch sound was coming from, and it was from the body.
So, im sure it would fit...but as far as operating it, i dont know how far that would go.