In the bowl of a food processor with steel blade, add lemon zest and sugar. Pulse until zest is finely minced into sugar. In a separate bowl, cream butter, and beat in sugar/lemon mixture. Add eggs one at a time, then lemon juice and salt. Mix until combined. Pour mixture into a 2-quart saucepan. Cook over low heat, stirring continuously, until thickened (at about 170°, just below simmer), about 10 minutes. Remove from heat; cool or refrigerate.