Add pineapple, mango, sugar, and lime juice to a blender. Blend on high until creamy and smooth, about 2-3 minutes.
Pour mixture in an ice cream maker and churn according to manufacturer's instructions. Most sorbet is done churning in about 10-15 minutes. The sorbet should have thickcened up to resemble a thick smoothie-like texture.
Once done, transfer sorbet to an airtight container.
Chill in the freezer for 4-6 hours, until fully frozen.
When you are ready to eat, allow the sorbet soften slightly at room temperature before serving.
Keep sorbet in an airtight container in the freezer for up to 2 weeks.
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