In a small saucepan, simmer 1/2 cup of the heavy cream with the ginger for about 10 minutes. Set aside.
In another small heavy saucepan, cook the sugar with the lemon juice over low heat, stirring frequently, until the sugar caramelizes to a light brown color, 10 to 15 minutes. Being careful to avoid splatters, stir in the remaining 2 tablespoons heavy cream. Remove from the heat.
Strain the cream into a bowl and whisk in the caramel until smooth. Serve warm.
The sauce will keep refrigerated for up to 1 month. Rewarm over low heat before serving.