In a medium heavy-bottomed saucepan, heat sugar, lemon juice, and 1/2 cup water over low heat until sugar dissolves. Bring syrup to a boil, and continue to boil, without stirring, until it begins to turn golden around the edges. It is important not to stir, as the syrup may crystallize.
Meanwhile, combine butter and heavy cream in a small saucepan. Heat until butter melts. When syrup begins to color, lower heat a bit, and continue boiling to a deep-golden color. It will darken rapidly. Remove pan from heat, and let it cool for 30 seconds. Add butter-and-cream mixture, being careful as the syrup will bubble up in the pan. Place pan back over heat, stirring until caramel is completely dissolved. Let sauce cool, taste, and add a pinch of salt, if necessary. Serve hot or chilled.