Make the lemon curd: In a bowl set over a pan of simmering water, whisk together lemon juice, butter, sugar, eggs and salt until butter melts and mixture thickens and coats back of a wooden spoon, about 25 minutes (do not let it boil). Strain through a fine-mesh sieve into another bowl and stir in zest. Cover with plastic wrap, pressing directly onto surface, let cool to room temperature, then refrigerate until chilled.
Make cake: Preheat oven to 350°F. Mist 2 8-inch round cake pans with cooking spray and line with parchment paper. In a medium bowl, whisk together flour, baking powder and salt. Using an electric mixer on medium speed, beat butter until soft. Gradually add sugar and lemon zest and beat until light and fluffy, about 5 minutes, stopping once to scrape down sides and bottom of bowl. Add eggs one at a time, beating well before each addition. Stir in ¹/3 of flour mixture, then half of sour cream. Repeat, ending with last ¹/3 of flour mixture. Stir in lemon juice.
Divide batter between pans, spreading evenly. Bake until a toothpick inserted in center of cake comes out clean, 25 minutes. Cool in pans on wire rack for 5 minutes, then turn out cakes onto rack to cool completely.
Make frosting: Using an electric mixer on medium speed, beat together butter, cream cheese and zest until light and fluffy. Scrape down sides and bottom of bowl with a flexible spatula. Gradually add sugar. Continue to beat until light and fluffy. Cover with plastic wrap and let sit at room temperature until the cake has cooled. If frosting becomes too warm, refrigerate it until it firms up, but don't allow it to become too stiff to spread.
Assemble cake: Using a serrated knife, carefully slice both cakes horizontally into 2 layers. Place one layer on a platter. Spread ¹/3 of lemon curd over cake. Top with second cake layer and spread with another ¹/3 of curd. Place third cake layer on top and spread with remaining curd. Top with final cake layer. Frost top and sides of cake. Chill cake for up to 2 hours before serving.