Answer:
Passover lambs were slaughtered no different than any animal was slaughtered according to the laws of kashrut. This means that the animal was restrained and the neck slit in one fast movement that severed the arteries resulting in almost instanteous loss of conciousness. The animal would then be hung by its hind legs to drain it of blood before it would have been prepared for eating.
There is no established tradition of hanging animals by their fore limbs.