Cool the cakes. Place the cakes on a wire rack and let cool 10 minutes. Flip the cakes out of the pans onto the rack, discard the parchment, and let cool completely, about 1 hour. Meanwhile, make the lemon curd. If you aren’t frosting the cakes right away, tightly wrap each cooled cake in plastic wrap to prevent them from drying out, then store at room temperature for up to 2 days.