Place the sugar, butter, lime juice, lime zest in the top of a double boiler; stir over medium-high heat until butter melts. Mix 2 tablespoons hot lime mixture into the eggs and stir to blend.
Reduce heat to medium until water simmers. Slowly whisk egg mixture into the lime mixture. Cook over the double boiler until lime mixture thickens and coats the back of a wooden spoon, 20 to 25 minutes. Cool slightly and spoon into a clean, glass jar. Cover and refrigerate.
