Sprinkle lamb all over with 1/4 tsp of the salt and pinch of the pepper.
In large Dutch oven, heat 2 tsp of the oil over medium-high heat; cook lamb, turning occasionally, until browned all over, about 5 minutes. Transfer to plate. Set aside.
In same pan, heat remaining oil over medium-high heat; cook onions, garlic and remaining salt and pepper, stirring, until softened, about 5 minutes. Stir in tomato paste and thyme; cook, stirring, until fragrant, about 1 minute.
Stir in vinegar, molasses, brown sugar and 1 1/3 cups water. Return lamb to pan; bring to boil. Cover and braise in 350°F oven until lamb is fork-tender, about 1 1/2 hours. Transfer lamb to a plate; keep warm. Discard thyme.
Skim from surface of cooking liquid. Bring cooking liquid to simmer and cook until reduced by half, about 10 minutes. Return lamb to pan; cook for 2 minutes.