Reading other people's opinions on this, I've thought of 2 ways for handle lives.
With lives, every life you lose you get put back close to where you died, similar to Conker's Bad Fur Day. You also keep your secondary collecting (notes) progress for that world. Losing all lives sends you back to the beginning of the world and you lose all note progress.
Without lives, you always keep note progression, but you're always sent back to the beginning of the world.
Yooka-Laylee should be its own game with its own feeling. It shouldn't try to be like Banjo-Kazooie, it shouldn't try to be like Donkey Kong, it should be like Yooka-Laylee.