Whisk together the sugar, egg yolks, pineapple purée, and lemon juice in a medium saucepan.
Heat over low-medium and bring to a low simmer. Simmer for about 10 minutes, stirring constantly, until thickened.
Add the coconut milk to a large bowl and whisk to break up any lumps and emulsify the milk.
Pour the thickened pineapple curd into the coconut milk in a slow stream, whisking constantly, until a homogenous mixture forms.
Cool the pineapple ice cream mixture in the refrigerator for at least an hour, or until cold to the touch, before churning according to ice cream maker instructions.
After churning, either serve immediately (it will melt quickly) or freeze in a sealed container for up to a month. This ice cream doesn't harden rock-solid when frozen, but still benefits from a few minutes at room temperature before scooping.
Notes
If you want a piña colada flavour, add a shot of rum to the coconut milk before whisking the pineapple curd into it.