Using a carrot peeler, remove the zest of 3 lemons, being careful to avoid the white pith. Put the zest in a food processor fitted with the steel blade. Add the sugar and pulse until the zest is very finely minced into the sugar.
Cream the butter and beat in the sugar and lemon mixture. Add the eggs, 1 at a time, and then add the lemon juice and salt. Mix until combined.
Pour the mixture into a 2 quart saucepan and cook over low heat until thickened (about 10 minutes), stirring constantly. The lemon curd will thicken at about 170 degrees F, or just below simmer. Remove from the heat and cool or refrigerate.