Preheat oven to 325°F
To prepare the crust, crush the graham crackers in a food processor. Alternatively, you can put them in a resealable gallon-sized bag and use a rolling pin to crush them. Add 3 tablespoons of applesauce to the graham crumbs (and sweetener if using) and thoroughly mix. The mixture should resemble wet sand at first and then turn into a dough ball. Add another tablespoon or two of applesauce if needed.
Spread the graham cracker crust into the bottom of a greased or lined 9-inch springform, cake pan, or pie pan. Bake the cheesecake crust for about 7 to 9 minutes so that it firms up a bit. Set aside to partially cool.
For the cheesecake filling, use a paddle attachment in a stand mixer to mix the softened cream cheese until smooth. Once there are no lumps, add the Greek yogurt, sweetener, salt, and pudding mix.
Mix the cheesecake batter over medium speed until completely smooth, stopping and scraping the sides in between to ensure all lumps are worked out.
Add the lemon juice and eggs and mix until combined. Do not over-mix because it will whip too much air into it.
Pour the cheesecake batter into the par-baked crust. Transfer the cheesecake to the oven and bake for about 35 to 45 minutes. Once it is mostly set but the center still jiggles, turn the oven off and leave the cheesecake in there for about another 20 minutes.
Remove the cheesecake from the oven and allow it to cool to room temperature. Then, move it to the refrigerator to cool for two hours minimum before serving.
For the optional blueberry compote, heat frozen blueberries over medium heat to soften them, then add the sweetener and salt. Mix the cornstarch into the lemon juice and water to dissolve it, then stir it into the blueberry mixture. Cook the mixture and remove it from the heat once thickened.