01 - Preheat oven to 350°F. Grease and line three 8-inch round cake pans with parchment paper.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
03 - In a large bowl, beat butter and sugar with an electric mixer until light and fluffy, 3 to 4 minutes.
04 - Add eggs one at a time, beating well after each addition. Mix in lemon zest and vanilla extract.
05 - Mix in lemon juice. On low speed, add flour mixture in three additions, alternating with milk, beginning and ending with flour. Mix until just combined.
06 - Divide batter evenly between prepared pans. Smooth the tops.
07 - Bake for 22 to 25 minutes, or until a toothpick inserted in the center comes out clean.
08 - Let cakes cool in pans for 10 minutes, then turn out onto wire racks to cool completely.
09 - Beat butter until creamy. Gradually add powdered sugar, beating until smooth and fluffy.
10 - Add strawberry puree, lemon juice, vanilla, and salt. Beat until well combined. If the frosting is too thin, add more powdered sugar; if too thick, add a splash of milk.
11 - If desired, trim cake layers for evenness. Place one layer on a serving plate. Spread with a thin layer of strawberry jam if using, then with buttercream.
12 - Repeat with second layer. Top with final cake layer and frost the top and sides with remaining buttercream.
13 - Decorate with fresh strawberries and lemon zest as desired. Chill for at least 30 minutes before slicing for best results.