Preheat the oven to 325 degrees. Grease and line an 8-inch loaf pan with parchment paper, set aside.
Grate the lemons and reserve the rind, being careful not to include the white bitter pith. Juice one lemon and combine with the 3 Tbs sugar; set in a warm place to create a syrup and set aside.
Cream the butter with the rest of the sugar and salt until fluffy, and add the eggs gradually, beating thoroughly to combine. Stir in the lemon rind and flour, then beat thoroughly for 3 minutes or so. (The longer you beat, the softer the cake.) Add the milk, then beat again.
Pour the cake into the pan and bake for 50-60 min. It is done when the cake springs back when gently pressed. Immediately prick the top with a fork or skewer and pour the lemon juice syrup all over the top. Cool in the pan.