Preheat oven to 350°. Grease and flour a 10-in. fluted tube pan. In a large bowl, cream butter and sugar until light and fluffy. Add 1 egg at a time, beating well after each addition. Beat in lime zest, vanilla and lime juice. Add flour alternately with milk, beating well after each addition. Transfer to prepared pan.

Bake until a toothpick inserted in center comes out clean, 1-1/4 to 1-1/2 hours. Cool in pan 10 minutes before removing to a wire rack to cool completely. For frosting, in a large bowl, beat cream cheese, butter, lime zest and lime juice until smooth.