Place 1 1/2 cups raspberries in container of an electric blender; cover and process until smooth. Pour raspberry puree into a wire-mesh strainer; press with back of spoon against the sides of the strainer to squeeze out juice. Discard pulp and seeds remaining in strainer. Combine raspberry juice and sugar, stirring until sugar dissolves.
Peel bananas; slice each banana diagonally into 4 pieces. Place banana in a bowl; add lemon juice, and toss gently. Arrange banana and remaining 1/2 cup raspberries evenly on 2 dessert plates. Spoon raspberry sauce evenly over fruit.