Combine raspberries, ¼ cup granulated sugar, water, and lemon juice in a saucepan. Cook over medium-low heat, stirring until berries release juices
Increase to medium heat and simmer, stirring constantly until slightly thickened.
Strain sauce into a bowl, retaining 2 tablespoons of seeds. Add reserved seeds back to the sauce.
Preheat oven to 325°F (165°C)
In a bowl, mix graham cracker crumbs, light brown sugar, and melted butter until evenly combined.
Press mixture into a 9-inch springform pan using a glass to level. Chill crust while making filling.
In a large bowl, beat cream cheese and brown sugar until smooth.
Add sour cream, vanilla extract, and room temperature eggs, mixing on low until fully incorporated.
Pour cooled raspberry sauce into the center of the cheesecake, gently swirling with a knife to avoid mixing it into the filling.
Bake for 55 minutes or until the center is just set.
Cool at room temperature before refrigerating for at least 4 hours, preferably overnight, to set completely.
Release springform pan and slice carefully before serving.