TheFork users who ate in Rome have said really good things about Schietto cucina alla mano, Gandhi and Ristorante Indiano OM. Maybe you should give them a try!
Some of the more popular Lamb restaurants where you can go with your friends in Rome according to TheFork users include:
Schietto cucina alla mano, with a 9.3 rating
Gandhi, with a 9.3 rating
Ristorante Indiano OM, with a 9.4 rating