Lightly coat a 1- to 1 1/2-quart soufflé dish or casserole* with cooking spray; line bottom with parchment paper. Cut a 27x18-inch piece of heavy foil in half lengthwise; fold halves lengthwise into thirds. Crisscross strips and place dish in center of crisscross.
Remove 1 teaspoon zest and squeeze 2 tablespoons juice from lemon. In a large bowl beat cream cheese with a mixer on medium for 30 seconds. Beat in the next three ingredients (through vanilla) until combined. Beat in eggs and lemon juice on low just until combined. Stir in lemon zest. Pour into prepared dish and cover tightly with additional foil.
Pour the warm water into a 5- to 6-quart slow cooker. Use foil strips to transfer dish to cooker (leave strips under dish).
Cover and cook on high about 2 1/2 hours or until center is set. Use foil strips to carefully remove dish from cooker; discard strips. Cool cheesecake, uncovered, on a wire rack. Cover and chill 4 to 24 hours.
About 1 1/2 hours before serving, prepare sauce. Place raspberries in a blender or food processor; cover and blend or process until smooth. Press berries through a fine-mesh sieve; discard seeds. In a small saucepan stir together the 2 1/2 teaspoons sugar and cornstarch; stir in pureed berries. Cook and stir over medium heat until thickened and bubbly. Cook and stir 2 minutes more. Transfer to a serving dish. Cover and chill at least 1 hour.
To serve, loosen and remove cheesecake from dish; peel off paper. Cut into wedges. Top with sauce and, if desired, additional fresh raspberries.
Before beginning this recipe, check to make sure that the soufflé dish or casserole you plan to use fits into your slow cooker.