Mix graham cracker crumbs, sugar, and melted butter. Press into the bottom of a greased 7-inch springform pan. Freeze while you prepare the filling.
In a small saucepan over medium heat, cook blackberries, sugar, and lemon juice until berries break down and mixture thickens (about 5 minutes). Mash with a fork and strain seeds if desired. Let cool.
In a mixing bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, then mix in sour cream, flour, lemon juice, lemon zest, and vanilla. Do not overmix.
Pour cheesecake filling over the crust. Spoon blackberry sauce in small dollops over the top and swirl with a toothpick or knife.
Pour 1 cup of water into the Instant Pot. Place a trivet inside and set the springform pan on top. Cover pan tightly with foil.
Pressure cook on High for 35 minutes, then let pressure release naturally for 15 minutes before opening the lid.
Remove the cheesecake, uncover, and let cool to room temperature. Refrigerate at least 4 hours or overnight before slicing.