Heat oven to 350°F. Grease a 9×5-inch loaf pan and line with parchment.
Whisk flour, baking powder, and salt in a bowl. Set aside.
Beat butter, cream cheese, and sugar until very fluffy, 2–3 minutes.
Beat in eggs one at a time. Mix in lemon zest and vanilla.
Stir the lemon juice into the yogurt until smooth.
Add dry ingredients in thirds, alternating with the yogurt mixture. Start and end with dry.
Spread batter into the pan and smooth the top.
Bake 50–60 minutes until a tester comes out clean. Tent if browning early.
Cool 10 minutes in the pan. Lift out and cool completely on a rack.
Whisk powdered sugar, lemon juice, and milk until glossy. Drizzle over cooled loaf and let set.