Preheat oven to 350°F. Grease and flour two 9-inch round cake pans.
In a large bowl, combine cake mix, pudding mix, oil, water, eggs, sour cream, and lemon zest. Beat until smooth.
Toss chopped strawberries in flour and gently fold into the batter.
Divide batter evenly between the pans and bake for 25–30 minutes or until a toothpick comes out clean.
Cool the cakes in the pans for 10 minutes, then transfer to wire racks to cool completely.
To make the frosting, beat butter and cream cheese until fluffy. Add powdered sugar, lemon juice, and vanilla, and beat until smooth.
Frost the cooled cakes and stack. Garnish with strawberries on top.