Make lemon syrup: In a small saucepan, bring 1/4 cup sugar, lemon juice, and 1/4 cup water to a boil over medium heat, stirring to dissolve sugar. Let cool completely, then brush over both sides of cake slices. Quarter each slice.
With an electric mixer, beat cream cheese with remaining 1/3 cup sugar on high speed until lightened. With mixer on medium speed, gradually add heavy cream in a steady stream; continue beating until mixture is light and airy (mixture will be like a very soft whipped cream).
Arrange half the cake pieces in the bottom of a 2-quart serving dish. Spoon half the cream-cheese mixture over cake in dollops; spread to sides of dish. Scatter half the blueberries and raspberries on top. Repeat layering with remaining cake, cream-cheese mixture, and berries, piling berries in the center.
Cover, and refrigerate until chilled, at least 1 hour and up to overnight.