Heat the oil in a large pot over medium heat. Add the lamb cubes and brown them on all sides, about 8 minutes total. Work in batches if needed to avoid crowding the pot.
Add the diced onion to the pot and cook until it softens, about 5 minutes.
Pour in the broth, then add the salt and pepper. Bring the mixture to a gentle simmer, cover the pot, and cook for 1 hour.
Stir in the sliced carrots and continue simmering, uncovered, for 30 more minutes until the lamb is tender and the carrots are soft but not falling apart.
Remove the pot from the heat and stir in the chopped fresh dill just before serving.