Combine the sugar, water, and lemon juice in a medium heavy saucepan and cook over medium-high heat, stirring, until the sugar dissolves. Let boil without stirring until the mixture becomes a deep amber color, 2 to 3 minutes, watching closely so it doesn't burn. Add the cream (be careful; it will bubble up), whisk to combine, and remove from the heat.
Add 2 tablespoons of the milk, then add up to 2 more tablespoons, until the desired consistency is reached. Let cool until just warm before serving. (The sauce will thicken as it cools.)
Yield: a generous 3/4 cup