Preheat oven to 350 degrees. Butter and flour a 10-inch Bundt pan.
Beat the butter using an electric mixer with a paddle attachment until light and smooth.
Add cream cheese and beat until smooth.
Add sugar gradually and beat for 3 minutes. Add lemon juice, zest, and vanilla. Mix well.
Beat in eggs 2 at a time, scraping down sides of bowl once or twice.
Add flour and salt and beat just until evenly mixed.
Pour into prepared pan. Bake for 1 1/2 hours or until toothpick inserted in center comes out clean.
Cool on wire rack for 15 minutes and then invert cake onto a cake stand or serving platter.
To make frosting, beat together melted butter and confectioners' sugar. Add in lemon juice and vanilla extract. Beat until smooth. Thin with milk if too thick.
Let cake cool almost to room temperature before frosting. Spoon frosting on top of cake so that it drips down edges.
Notes
The most important part of making a pound cake is thoroughly beating the butter and sugar, or in this case the butter, cream cheese, and sugar. You want to really give it time to become light and fluffy. During this process air is whipped into the mixture and this is what helps the cake rise and develop a wonderful texture.Once you add the flour, beat as little as possible.