Preheat oven to 350°. Coat a 9-inch springform pan with cooking spray. Pulse graham crackers in a food processor until finely ground. Add oil and water; pulse until clumps form. Press crumbs into bottom and 1 inch up side of pan. Bake until fragrant (about 10 minutes). Cool on rack. Reduce oven temperature to 325°.
Process raspberries in food processor with 2 tablespoons sugar until smooth. Strain purée into a small saucepan. Boil mixture for 3 minutes, until slightly thickened. Cool to room temperature.
In the bowl of an electric mixer, beat cream cheese and remaining 1 1/4 cups sugar until smooth (about 5 minutes). Add sour cream and beat until just combined. Add eggs then egg whites, one at a time, beating after each addition to incorporate. Add flour, vanilla, lemon zest, and salt, and mix until combined.
Pour batter into prepared pan, then place cheesecake into a roasting pan. Drop teaspoons of raspberry purée all over top of cheesecake. Using a wooden skewer or knife, swirl the purée. Place roasting pan in oven and add hot water to roasting pan to a depth of 2 inches.
Bake until cake is set but the center still jiggles (about 1 hour, 10 minutes). Turn off oven. Cool cheesecake in closed oven for 30 minutes. Remove springform pan from water bath. Run a knife around inside edge of pan; cool to room temperature. Chill until firm (at least 6 hours) before unmolding.