Combine the water, lemon juice, and cranberries in a medium saucepan. Bring to a boil. Reduce heat and simmer for 5 minutes or until the cranberries pop. Place the cranberry mixture in a blender or food processor, and process until smooth. Strain the cranberry mixture through a fine mesh strainer over a bowl, then discard the solids.

Combine the granulated and brown sugar and butter in a mixing bowl, and beat with a mixer at medium speed until well combined. Add the 2 egg yolks and egg, 1 at a time, beating well after each addition. Stir in the cranberry mixture, cornstarch, and salt. Place the mixture in the top of a double boiler. Cook over simmering water until a thermometer registers 160° and mixture thickens, about 10 minutes, stirring frequently. Remove from heat and let stand for 5 minutes. Stir in the liqueur. Cover and refrigerate before serving. Will keep in the refrigerator for up to 1 week.