Combine berries and ½ cup sugar; let stand about 1 hour. Drain juice; there should be 1 cup. Add ½ cup water and lemon juice; heat. Add gelatin, softened in ¼ cup water; stir until gelatin dissolves. Cool until partially set.
Place sweetened berries in corn-flake crust; pour over gelatin mixture; chill until firm. Spread with sweetened whipped cream.
Combine crushed cornflakes, sugar, and butter. Press into 8-inch pie pan. Chill.