In a large bowl, season flour with salt and pepper. Dredge lamb in flour mixture, shaking off excess. In a Dutch oven, heat oil over medium heat. Working in batches, brown lamb on all sides, about 5 minutes per batch. Transfer to a plate.
Pour 1/4 cup water into pot, scraping up browned bits from bottom with a wooden spoon. Add onion; cook, stirring occasionally, until water has evaporated and onion is beginning to soften, about 5 minutes. Return lamb to pot; stir in thyme, beer, and 1 1/2 cups water. Cover; simmer until lamb is tender, 1 to 1 1/2 hours.
Add potatoes, carrots, and 1/2 cup water. Cook, covered, until vegetables are tender and stew has thickened, about 20 minutes. Season with salt and pepper. Let cool completely before storing. Stir in parsley just before serving.