Cut the butter into small pieces, and toss into a food processor fitted with a steel blade, along with the flour, sugar, and salt. Pulse until the texture is like very coarse meal.
Pour in the milk or water a tablespoon at a time, pulsing until the dough comes together in a ball. Be careful not to add too much liquid, or the dough will be impossible to roll out.
Shape the dough into a disk, cover with plastic wrap, and refrigerate for at least 45 minutes. Roll out the piecrust, and line an ungreased 9-inch tart pan with it. Prick it all over with a fork, and bake for 15 minutes, or until golden brown. (This can be done ahead of time.)
To make the filling
Pour 2 cups water into a heavy medium-sized saucepan. Add 1 cup of the sugar, and bring to a boil.
Slice one of the lemons into thin circles, drop them into the boiling sugared water, lower the heat, and simmer for about 30 minutes, uncovered. Drain, and discard the liquid.
Grate the zest of the remaining 3 lemons to get 2 tablespoons of zest, then juice the lemons to get about ¾ cup juice.
Whip the eggs and remaining sugar in the bowl of an electric mixer at medium speed. Gradually add the lemon juice and zest.
Pour the filling ingredients into a medium saucepan, add the butter or margarine, and cook over medium heat, stirring constantly, being careful not to boil, until the lemon thickens into a curdlike custard, about 5 minutes.
Spoon the filling into the prebaked crust. Lay the lemon slices all over, and refrigerate until firm.