Preheat oven to 350°F. Whisk cake flour, baking powder, and salt together.
Beat softened butter until smooth. Add cream cheese and beat until combined. Add sugar and beat about 2 minutes until light and fluffy.
Beat in eggs one at a time. Add vanilla, almond extract, lemon zest, and lemon juice.
Add dry ingredients in three parts, mixing just until combined after each.
Thoroughly coat a Bundt pan with cake release spray. Pour in batter and bake 75–85 minutes, until a toothpick inserted in the center comes out clean.
For icing, beat softened butter until smooth. Add cream cheese and beat on high for 2 minutes. Mix in powdered sugar in three parts, then lemon zest, lemon juice, and salt until smooth and pourable.
Cool cake in pan for 10–15 minutes, then invert onto a serving plate. Pipe or spread icing over the still-warm cake and let set before slicing.