Zest the lemons. Be careful to avoid the white pith as it is very bitter.
Add the sugar and lemon zest to a food processor fitted with the steel blade and pulse until the zest is finely ground up with the sugar.
In a medium glass or stainless steel mixing bowl, cream the butter and lemon sugar until fluffy. Add the eggs, one at a time, and beat until combined. Add the lemon juice and salt and beat until combined.
Pour the mixture into a medium stainless steel saucepan and cook over low heat stirring continuously until thickened and the temperature has reached 170 F, about 20 minutes. Check the temperature using a candy thermometer.
Remove from the heat, cool, and refrigerate. It will keep in the fridge for a week and can then be frozen for up to 2 months.