According to an interview in the December issue of retro gamer.
The real reason Dizzy 2 has one life is actually because of a problem that could occur.
Say if you dropped the snorkel underwater, you would instantly drown again if you restarted in the water.
But even if you started on the beach. You wouldn't be able to get back in the water again. The game would be impossible to finish.
So... the Olivers were running out of time and had no ideas how to fix it the lives were reduced to 1. Right at the last minute. Up until then the game had 3 lives just like dizzy 1!