According to everything I have read, this lion isn’t really black. It’s a hoax, a Photoshop manipulation. It is however, not a genetic impossibility. Color mutations among creatures great and small are never impossible. This particular picture originally showed (supposedly) a very rare white lion that has been manipulated to appear black.
I’m not sure why showing an extremely rare white lion would be less intriguing than a black one, but there you go. It doesn’t have to make sense.