Mix together milk and lemon juice and let stand until milk curdles, about 1 minute.
Whisk together flour, baking powder, salt, and baking soda in a bowl.
Beat together butter and sugar in a large bowl with an electric mixer at high speed until pale and fluffy, about 2 minutes. Add eggs, 1 at a time, beating until combined, then beat in bananas until combined. (Mixture will look curdled.)
Add flour mixture to banana mixture alternately with milk, mixing at low speed just until batter is smooth. Stir in walnuts. Pour into loaf pan and bake until a wooden pick or skewer inserted in center of bread comes out clean, about 1 hour.
Cool bread in pan on a rack 20 minutes, then invert bread onto rack. Remove paper and turn bread right side up on rack to cool completely.