Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9-inch springform pan.

Combine slivered almonds, 1/3 cup white sugar, 1/4 cup butter, and milk in a small saucepan over low heat; cook and stir until butter is melted and mixture is smooth, 3 to 4 minutes. Remove topping from heat.

Combine 1 1/2 cup flour, cream of tartar, and salt in a bowl.

Beat 3/4 cup softened butter and almond paste in a large bowl using an electric mixer until creamy. Gradually add 1 cup white sugar and continue beating until mixture is light and fluffy, about 5 minutes. Beat in eggs one at a time, beating 1 minute after each addition; stir in lemon juice, lemon zest, and vanilla extract. Add flour mixture and beat until batter is just mixed, about 1 minute more; pour into the prepared pan and smooth the top.

Sprinkle remaining 1 tablespoon flour evenly over batter. Spoon the topping over the flour layer.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, 45 to 50 minutes. Cool on a wire rack.