In a small bowl, combine graham cracker crumbs, melted butter, and sugar until it gets sticky and resembles wet sand. Press mixture into bottom and sides of tart shell. Bake crust until it darkens, about 15 minutes. Set aside until cool.
In a bowl or stand mixer with paddle, beat together cream cheese, sour cream, and light brown sugar until smooth and fluffy and sugar has dissolved and is no longer grainy. Stir in vanilla, lemon zest, and lemon juice.
Spread lemon filling evenly over cooled tart crust. Line outer edge of tart with strawberries. Pile blueberries into the center of the ring of strawberries.
Put apricot jam and water in a small bowl and mix to combine. Microwave until thinned out, about 20 seconds. Brush berries with apricot glaze. Let tart chill in refrigerator for one hour before serving.