Add berries and the lemon juice to a blender or food processor fitted with the chopping blade; blend or process until fairly smooth.
Transfer to a fine-mesh sieve set over a big bowl; gently press the puree against the mash with the back of a wooden spoon to extract as much of the juice and pulp as possible, leaving the skins behind.
Discard the mass in the sieve and set the puree aside.
Heat the milk and cream in a saucepan over medium heat until tiny bubbles fizz around the pan’s inner rim; adjust heat to maintain this temperature without letting the mixture boil.
Beat the egg yolks and sugar in a medium bowl with an electric mixer at medium speed until pale yellow, thick and grainy, about 2 minutes.
Whisk about one quarter of the hot milk mixture into the egg yolk mixture until smooth, then whisk this combined mixture into the remaining hot milk mixture in the pan.
Immediately decrease heat to low; cook slowly, stirring constantly, until the mixture thickens to the consistency of melted ice cream and can coat the back of a wooden spoon, about 4 minutes.
Strain through a clean fine-mesh sieve into a medium bowl to remove any bits of scrambled egg; stir in the blueberry puree, vanilla, and salt.
Refrigerate until cold, about 4hours or overnight.
Freeze the custard in your ice cream machine according to manufacturer’s directions.
Serve at once or scoop into a freezer container; store in the freezer for up to 1 month; soften at room temperature for up to 10 minutes before serving.