Cooking the lemon juice in this recipe tones down its acidity and concentrates its flavor.
Prepare an ice bath. Place lemon juice in a small saucepan set over medium heat. Boil until reduced by half, about 12 minutes. Add sugar; stir until dissolved, about 4 minutes. Remove from heat. Stir in the buttermilk, cream, corn syrup, salt, and candied lemon zest. Chill over the ice bath or overnight in the refrigerator.
Freeze mixture in an ice-cream maker, according to manufacturer's directions. Place in an airtight container in the freezer; store up to 1 month.