Place blueberries, ¼ cup sugar and lemon juice in a medium saucepan. Cook over low heat, stirring occasionally, until the blueberries release their juices and begin to cook down (about 20 minutes). You can help this process along a bit by gently mashing the berries each time you stir. Drain using a fine mesh basket strainer, pressing berries to squeeze out as much juice as possible. Set aside.
Prepare an ice bath in a large bowl and have another strainer ready. Add heavy cream to a medium sized bowl and set aside.
Heat half and half and 1 cup sugar in a different saucepan over low heat, stirring to dissolve the sugar. Remove from heat once you see steam rising from the surface and the mixture is completely heated through.
Meanwhile, whisk 5 egg yolks in a bowl until slightly thickened. Slowly, while whisking, add ½ cup of the warm half and half mixture to the yolks. Once the ½ cup is incorporated, whisk in the remaining half and half mixture. Return the half and half-yolk mixture to the saucepan, cook over medium heat, stirring constantly with a wooden spoon. You will know the custard is thick enough when you see steam rise from the surface and the custard coats the spoon. Strain the custard into the bowl with the heavy cream. Stir to combine.
Add the blueberry mixture to the custard mixture and stir. Place the bowl in the ice bath and stir occasionally to cool (be sure not to get any water in your custard mixture). Refrigerate until cold.
Freeze custard in an ice cream maker according to the manufacturer’s instructions.