Zest outer yellow peel of the lemons, avoiding the white pith. Then juice the lemons.
In a food processor pulse the sugar and 1 tablespoon of lemon zest until finely ground.
Add the butter the the food processor and cream thoroughly. Then add 1/2 cup of lemon juice, salt, and eggs one at a time until combined.
Pour the mixture into a 2-quart sauce pot on stove top and heat on medium-low, stirring until it begins to simmer and thicken. Once it reaches 170 degrees on a candy thermometer, remove from heat. (This takes approximately 8-10 minutes.)
Serve warm on your favorite baked goods or chill and serve as desired.
Store in a tightly sealed container in refrigerator for up to 1-2 weeks.