Cook juniper berries in a small skillet on high heat for 2 minutes. Crush berries with the back of a spoon. Add water and lemon juice; bring to a boil. Cook 5 minutes or until mixture is reduced by half. Strain mixture, discarding solids.
In a food processor or blender, process lemon-juniper mixture, hot sauce, and next 3 ingredients until smooth, stopping to scrape down sides. With processor or blender running, add oil in a slow steady stream, blending until thickened.