hours in advance – strain the yogurt. Fit a sieve over a bowl and line it with two layers of cheesecloth. Pour the yogurt into the sieve, cover with plastic wrap, and refrigerate for 6 to 8 hours to drain. Discard the liquid, and measure out 1 ¼ cups of the drained yogurt; set aside.
Make the blueberry sauce. Mix the blueberries and sugar in a small saucepan and bring to a boil over medium heat. Reduce the heat and simmer, stirring occasionally, until the berries are tender and the sauce is thickened, about 8 minutes. Remove from the heat and let cool, then refrigerate until cold before using.
Make the lemon syrup. Using a vegetable peeler, remove the zest in large strips from 1 lemon; reserve for the frozen yogurt (leave the lemon zest in large strips so it's easier to strain out later). Juice enough of the lemons to make ½ cup. Combine the lemon juice and sugar in a small saucepan and bring to a boil over medium-high heat, stirring to dissolve the sugar. Remove from the heat and let cool.
Mix the yogurt base. Mix about 2 tablespoons of the milk with the cornstarch in a small bowl to make a smooth slurry. Whisk the cream cheese in a medium bowl until smooth.
Fill a large bowl with ice and water.
Cook the ingredients. Combine the remaining milk, the cream, sugar, corn syrup, and lemon zest in a 4-quart saucepan, bring to a rolling boil over medium-high heat, and boil for 4 minutes. Remove from the heat and gradually whisk in the cornstarch slurry. Bring the mixture back to a boil over medium-high heat and cook, stirring with a heatproof spatula, until slightly thickened, about 1 minute. Remove from the heat.
Combine and chill the ingredients. Gradually whisk the hot milk mixture into the cream cheese until smooth. Add the reserved 11/4 cups yogurt and the lemon syrup and whisk until smooth. Pour the mixture into a 1-gallon Ziploc freezer bag and submerge the sealed bag in the ice bath. Let stand, adding more ice as necessary, until cold, about 30 minutes.
Combine the lemon yogurt with blueberry sauce. Remove the zest from the frozen yogurt base. Pour into the frozen canister and spin until thick and creamy. Pack the frozen yogurt into a storage container, alternating yogurt with layers of the chilled blueberry sauce. End with a spoonful of sauce; do not mix. Press a sheet of parchment directly against the surface, and seal with an airtight lid. Freeze in the coldest part of your freezer until firm, at least 4 hours.