Preheat the oven to 350°F (177°C). Grease and line two 8-inch cake pans with parchment.
In a bowl, whisk flour, baking powder, and salt. In another bowl, whisk butter and sugar until light and fluffy. Beat in eggs one at a time, then stir in lime zest, lime juice, and vanilla.
Alternate adding dry ingredients and milk to the wet ingredients, beginning and ending with dry ingredients. Mix until just combined. Divide batter between pans.
Bake for 22 to 28 minutes, until a toothpick comes out with a few crumbs. Let cakes cool completely before frosting.
For the frosting, beat butter until creamy. Gradually add powdered sugar, then lime juice and lime zest. Beat until smooth and fluffy. Frost cooled cake layers and chill briefly to set.
Notes
Light and bright lime cake perfect for spring and summer gatherings.