Make the raspberry coulis: Combine thawed raspberries and sugar in a microwave-safe bowl. Heat 2 minutes, stir, taste, and adjust sweetness.
Blend the mixture until smooth, strain through a fine mesh sieve, and chill.
Make the vanilla cake: Preheat oven to 350°F (175°C). Grease and line a 9-inch springform pan.
Beat sugar, egg, vanilla, and oil. Mix dry ingredients separately and combine with wet ingredients, alternating with milk.
Pour batter into pan and bake for 18 minutes. Cool and refrigerate.
Prepare the cheesecake: Lower oven to 325°F (160°C). Place a water bath pan in the oven.
Beat cream cheese and sugar until smooth. Add cream, lemon juice, flour, zest, extract, food coloring, then eggs one at a time.
Pour batter over prepared pan, bake 65 minutes, then cool in the oven for 1 hour. Refrigerate overnight.
Assemble: Place cake layer in pan, dip ladyfingers in coulis, layer over cake, add cheesecake layer upside down, chill overnight.
Make topping: Bloom gelatin in water. Whip cream with sugar and lemon extract. Add gelatin. Spread on cake and chill.
Decorate with raspberries, lemon slices, and zest. Slice and serve with extra coulis.