Take the train to Viterbo from Piazzale Flaminio and get off at Saxa Rubra. You can use the ordinary 75 minute ticket or your travel card. From the coach station buy the ticket to Fiano Romano. From the Via Flaminia the bus takes then the Via Tiberina along which is a bus stop right in front of the entrance to Lucus Feroniae. Some bus drivers, however, may not know about it.
Entrance is free.
It's located along the railway line on the way to Saxa Rubra at Campi Sportivi station which is rather isolated. Perhaps it is a better idea to get off at Acqua Acetosa instead, and take the Viale della Moschea by the pedestrian bridge over the railway. The big marble fountain on the way, beside a little bar, is the old Acetosa water spring. Until the beginning of the century this place was the destination for a Sunday afternoon trip for the inhabitants of Rome. Also, in previous centuries, the acquaiuoli, the Roman water sellers, used to come here with their donkeys and barrels to get water to sell in the City.