For the cake: Preheat the oven to 350 degrees F. Butter two 9-inch cake pans, then line the bottoms with parchment paper and butter the paper.
Combine the butter, granulated sugar, oil, lemon zest and vanilla together in a large bowl. Beat with an electric mixer until light and fluffy. Beat the eggs in, one at a time. Beat in the lemon juice.
Whisk the flour, baking powder and salt together in a bowl.
Add the flour mixture to the butter mixture in 3 batches, alternating with the milk and beginning and ending with the flour.
Divide the batter evenly between the two prepared cake pans. Bake in the center of the oven until a wooden pick inserted in the center comes out clean, 20 to 25 minutes. Cool in the pan for 10 minutes, then run a thin knife around the edges of the pans and invert onto racks to cool completely.
For the frosting and filling: Beat the butter, cream cheese, lemon zest and juice and vanilla together in a large bowl with an electric mixer until very smooth. Add the confectioners' sugar and beat until incorporated and smooth. Separate 1 cup of the frosting to a bowl. Mix the jam into the cup of frosting.
Spread the raspberry frosting on top of one cake layer. Arrange most of the raspberries on top (reserve 7 or 8 for the top of the cake). Carefully put the second cake layer on top. Take about 1 cup of the remaining plain frosting and use it to cover the entire cake in a thin, even layer (it is okay if it looks messy). Refrigerate the cake until the frosting is firm, about 20 minutes. Use the remaining frosting to evenly cover the cake. Mound the remaining raspberries in the center and serve.