Preheat the oven to 350 degrees F. Spray an 8-inch round cake pan with baking spray. Line the bottom with a piece of parchment and spray again.
Put the raspberries in a bowl and add the lemon juice and 1 tablespoon of the granulated sugar. Mash well and let sit a few minutes for the juices to release. Press through a mesh strainer to remove the seeds. Remove 2 teaspoons of the raspberry syrup for the frosting and set aside. Reserve the remaining raspberry syrup for the batter.
In a stand mixer with a paddle attachment, beat the eggs with the remaining 1 cup granulated sugar until light and fluffy, about 3 minutes. Beat in the cream, vanilla, lemon zest and remaining raspberry syrup.
Sift together the cake flour, baking powder and salt. Add the dry ingredients to the batter in 3 additions, mixing between each addition until just combined. Pour into the prepared pan and smooth out the top. Bake until a toothpick inserted in the center comes out clean, about 30 minutes. Let cool completely, then turn out onto a cake stand or serving plate.