Preheat oven to 350°F (175°C). Grease and flour three 8-inch round cake pans, then line the bottoms with parchment paper circles.
Make the strawberry compote first: Toss diced strawberries with 1/4 cup sugar in a bowl and let sit for 30 minutes. Transfer to a small saucepan and simmer over medium heat for 8-10 minutes until thickened, stirring occasionally. Let cool completely, then refrigerate.
Whisk together the cake flour, baking powder, and salt in a medium bowl and set aside.
Beat the butter and 1 3/4 cups sugar in a large bowl with an electric mixer on medium-high speed for 3-4 minutes until light and fluffy. Add eggs one at a time, beating well after each addition.
Mix in the lemon zest and lemon juice until combined. The mixture may look slightly curdled but will come together.
Add the flour mixture in three additions, alternating with the milk in two additions, beginning and ending with flour. Mix on low speed just until combined after each addition, scraping down the bowl as needed.
Divide batter evenly among the prepared pans and smooth the tops. Bake for 22-26 minutes until a toothpick inserted in the center comes out clean and the tops spring back when lightly pressed. Cool in pans for 10 minutes, then turn out onto wire racks to cool completely.
Make the frosting: Beat cream cheese and 1 cup butter together until smooth and creamy, about 2 minutes. Gradually add powdered sugar one cup at a time on low speed, then increase to medium-high and beat for 2-3 minutes until fluffy. Mix in heavy cream and vanilla extract.
Level the cake layers with a serrated knife if needed. Place one layer on a serving plate and spread with half the strawberry compote, leaving a 1/2-inch border. Add a thin layer of frosting over the compote. Repeat with the second layer, then top with the third layer.
Apply a thin crumb coat of frosting over the entire cake and refrigerate for 20 minutes. Spread the remaining frosting over the top and sides of the cake in a smooth or textured finish. Garnish the top with fresh strawberry slices and serve chilled.