Yes, that is Lily Allen on a proper zebra, in the official video for Lily's Air Balloon, shot in sunny South Africa, and directed by Noel and Stefan of That Go, going back to the very colourful and upbeat aesthetic of their early work.

Lily also gets what looks like genuinely up-close and personal with a cheetah (probably quite briefly), as the camera never stops moving - it's the eponymous air balloon, going airborne and then back down to earth. 

And what's more, Nelson Mandela gets a special credit...