Let the frozen mango sit at room temperature for 10 to 15 minutes so it blends easily.
Add the mango, water, sweetener, and lime juice to a blender. Blend until completely smooth with no visible chunks, scraping down the sides as needed. Taste and adjust sweetness — it should taste slightly sweeter than you want, since freezing mutes flavor.
Pour the purée into a Ninja Creami pint container, stopping at the max fill line. Secure the lid.
Freeze on a level surface for 24 hours.
Remove the lid, place the pint in the outer bowl, lock it into the Ninja Creami, and press SORBET.
The sorbet will likely look powdery after the first spin. Add 1 to 2 tablespoons of water or coconut milk and press RE-SPIN. Repeat once if needed.
Serve immediately, or press parchment against the surface and refreeze.