If you didn't realize, there are some mobs you can't put on leashes (such as villagers, wild wolves and ocelots, "monster" mobs, and bats, to name a few). I mean, I know, you can use a fishing pole instead, but that's not quite like a leash. You can't hold other stuff while leading this mob, the mob doesn't really follow you, and you can't tie it to a fence.
I would suggest that a leash should work on all mobs (outside of boss mobs or players of course), but it seems a little weird to put a mob like that on a normal leash.. So how about a chain instead?
Appearance: This appears just like a leash, but it's a little thicker and is a grey-silver with a chain-link instead of a "leash". The collar also appears to be made of metal like the rest of it.
Usage: It's used just like a leash, but any mob can be on it (this excludes the Ender Dragon, the Wither, and other players, however). Like a normal leash, it can be attached to fence posts or held by the player. Essentially, it's just like a leash.