Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving overhang on the sides for easy removal.
In a large bowl, mix the strawberry cake mix, oil, egg, egg yolk, vanilla, and lemon zest until a thick dough forms. Fold in the white chocolate chips.
In a small bowl, combine the chopped strawberries with 1 teaspoon sugar and 1/2 teaspoon vanilla. Let sit for 15 minutes, then drain off any excess liquid.
In a separate bowl, beat the cream cheese, 1/4 cup sugar, egg white, vanilla, and lemon zest until smooth. Fold in the drained strawberries.
Press half of the strawberry dough into the bottom of the prepared pan. Spoon the cream cheese mixture evenly over the top.
Drop spoonfuls of the remaining dough over the cheesecake layer and gently spread to partially cover.
In a small bowl, stir together the melted butter, brown sugar, flour, and sliced almonds. Sprinkle evenly over the top.
Bake for 30 to 34 minutes, or until the center is set and a toothpick inserted in the center comes out with a few moist crumbs.
Cool in the pan on a wire rack for 30 minutes, then refrigerate for at least 1 hour before slicing into 16 squares.