Heat the olive oil in a large Dutch oven over medium heat. Add the lamb cubes and brown them on all sides, about 6 minutes total. Remove the lamb and set it aside.
Add the onion, carrots, and garlic to the pot. Cook until the onion softens, about 4 minutes.
Stir in the sliced mushrooms and cook until they release their liquid and start to brown, about 5 minutes.
Return the lamb to the pot. Add the barley, beef broth, thyme leaves, salt, and pepper. Bring the mixture to a boil.
Reduce the heat to low, cover, and simmer for 45 minutes until the barley is tender and the lamb is cooked through.
Remove the pot from the heat. Slowly stir in the heavy cream until the stew turns creamy and smooth.