Simmer the diced fresh pineapple with 1/4 cup granulated sugar and lemon juice for 10 minutes, stirring occasionally, until softened and the juices look more concentrated. Remove from heat and cool slightly before blending to a chunky puree, leaving some texture behind.

Heat the heavy cream and whole milk until steaming, not boiling, then lower the heat as soon as steam rises. In a separate bowl, whisk the egg yolks with the remaining 1/2 cup granulated sugar until smooth.

Slowly whisk the steaming dairy into the egg yolks in a thin stream to temper, then pour everything back into the pot. Keep cooking while stirring until the mixture reaches 175F and coats the back of a spoon.

Strain the custard to remove any bits, then return it to the pot and stir in vanilla extract, salt, and the pineapple puree. Continue stirring until evenly combined and the color turns a pale yellow.

Cool the custard completely to room temperature, then refrigerate for 4 hours until very cold. The mixture should look thick when you tilt the container.

Churn in an ice cream maker according to the manufacturer’s directions until it thickens to soft-serve consistency, with a lighter, aerated texture. Scrape into a container and freeze until firm.