From the Novo Rio bus station in the city of Rio de Janeiro or from Niterói-RJ, buses leave by bus 1001 to Nova Friburgo (by the South bus station) or if you come by Teresópolis or north of Rio de Janeiro by the North bus station.
From the South bus station, take another bus to Lumiar (municipal company Faol).
By the North bus station you should take a bus to the city center and from there take the bus to Lumiar or São Pedro da Serra or even Boa Esperança.
By car, take BR 101, then RJ 116 (Rio-Nova Friburgo) to the Mury district.
This district is distant 24 km from the center of Lumiar by RJ 142 (total of the trip by RJ are of 2h and 30 min approximately).
There are also roads along the BR 101 entering by the Serra Mar road in Casimiro de Abreu or by Parada Modelo (Guapimirim) or even by Teresópolis or Rio de Janeiro.