Heat oven to 350. Spray a loaf pan, or muffin tin.
Cream the butter, sugar and lemon zest together; beat until fluffy.
Add eggs one at a time, beating well between. Add 1 cup of the flour and the salt, mix well. Add the lemon juice.
Add the second cup of flour, mixing well. Add the milk. Continue to mix until all ingredients are incorporated.
Pour into loaf pan or muffin tins. Bake until lightly browned and pulling away from the sides, or approximately 35-40 minutes for the loaf pan, 20-25 for muffin tin.
Remove from oven to cooling racks. Poke holes in the top.
Combine the remaining lemon zest with lemon juice. In a liquid measuring cup, put 1 cup of powdered sugar and, with a fork, beat in 1 teaspoon of the lemon juice. Continue to beat it well, until the lumps are removed. Add the remaining juice. Adjust thickness by adding powder and/or juice. Place cake on a serving plate and pour icing over the top of the warm cake.
NOTE: I make the icing very thin to start and pour it over the cake, allowing it to run into the holes and soak well. Then, I thicken it to about gravy thickness and drizzle it over. The two icing textures make an appealing presentation.
**We find 3/4 C of sugar is sufficient, however you may bump it up to 1 full cup if it doesn't satisfy your sweet tooth.