Place the raspberries in a food processor; cover and process until smooth. Press the puree through a fine mesh sieve to remove seeds (you should have 1 cup seedless puree).
Place apple juice in a large microwave-safe bowl. Sprinkle gelatin over apple juice; stir to moisten. Let stand 5 minutes. Stir in sugar and corn syrup. Microwave the mixture on high for 1 to 1 1/2 minutes or until gelatin is dissolved, stopping and stirring frequently.
Stir raspberry puree and lemon juice into the gelatin mixture. Pour mixture into a plastic wrap-lined 8x8x2-inch baking pan. Cover top of pan with waxed paper. Chill until set, 2 to 3 hours.
Use plastic wrap to lift mixture from pan. Invert onto a cutting board; carefully pull back plastic wrap. Use a 1 1/2- to 2-inch heart-shaped cutter to cut shapes. Chill to store.