Add the cream cheese and powdered erythritol to the bowl of a stand mixer. Beat on medium speed until completely combined and smooth. Scrape down bowl as needed. With the mixer on, add the eggs one at a time to the bowl. Beat for 1 minute after each addition until the mixture is light and resembles a thick batter. Add the lemon juice, zest and vanilla and beat until combined.
Pour the batter into the prepared springform pan and smooth the top. Wrap bottom of pan with foil to prevent leaks. (optional) Set aside.
Rinse out food processor and replace bowl. Place raspberries into bowl with erythritol. Set aside a handful of raspberries to use for garnish later. Pulse until smooth and no raspberry chunks remain.
Set out a medium bowl. Over the bowl, transfer the raspberry mixture to a large strainer. Using a rubber spatula, push the raspberry puree through the strainer until only the seeds remain. Discard seeds. Use a spoon to add dollops of raspberry puree to the top of the cheesecake batter. Lightly drag a toothpick thru the puree to create a decorative design on top of the cheesecake.
Place pan on center rack of 325° oven and bake for 60 - 75 minutes, until outer perimeter of cheesecake is firm and only 2 - 3 inches in the center remains slightly jiggly when pan is lightly moved.
Remove cheesecake from oven and run knife around edge of cheesecake. Leave cake in pan, and cool on rack until room temperature. Lightly wrap cheesecake, still in pan, and chill in refrigerate until cheesecake is firm, about 4 - 6 hours or overnight.
To remove from pan, gently run a sharp knife again between cheesecake and ring of springform pan. Unlatch pan and lift ring off of cheesecake. Leave cake on pan bottom to serve. Top with reserved berries and any remaining puree.