Quinctius was elected consular tribune in 438 BC together with Mamercus Aemilius Mamercinus and Lucius Julius Iullus. They continued hostilities against the Fidenates and their leader Lars Tolumnius, which would result in the death of four Roman legates sent as ambassadors. The four legates, Gaius Fulcinius, Cloelius Tullus, Spurius Antius and Lucius Roscius, would later be honoured with statues on the Rostra.^{[3][4][5][6][7][8]}

In the following year, the war with the Fidenates was escalated and a dictator was appointed to handle the crisis. The dictator was the former consular colleague of Quinctius, Mamercus Aemilius Mamercinus. Aemilius selected Quinctius to be his second-in-command as magister equitum. They fought and defeated the Veii, Falerii and Fidenae, and Aemilius was granted a triumph.^[9][10]

In 428 or 427 BC Quinctius held the consulship together with Aulus Sempronius Atratinus. This consulship is dubious as it is only mentioned by Diodorus Siculus and is placed in between the consuls of 428 BC, Aulus Cornelius Cossus and Titus Quinctius Poenus Cincinnatus, and the consuls of 427 BC, Gaius Servilius Structus Ahala and Lucius Papirius Mugillanus. It is possible that they were suffect consuls replacing the college of 428 BC or that all four consuls mentioned in 428 BC were consular tribunes.^[11][12] All events described by other ancient authors are ascribed to the ordinary consuls of 428 BC.

Quinctius was re-elected as consular tribune in 425 BC together with Aulus Sempronius Atratinus, Lucius Furius Medullinus and Lucius Horatius Barbatus. They oversaw the signing of a twenty year truce with Veii and a three year truce with the Aequi.^{[13][14][15][16]}

Quinctius, or his brother Titus, was elected as consular tribune in 420 BC. Livy and the Chronograph of 354 has Lucius Quinctius, while the Fasti Capitolini points towards Titus. Scholars generally favour Lucius Quinctius as the consular tribune of 420 BC and that the Fasti has confused the two brothers. The college, including Quinctius, consisted of two of his former colleagues from 425, Furius and Sempronius, and a consular newcomer, Marcus Manlius Vulso. Little is known about the events of the year other than that Sempronius presided over the election of the Quaestors.^{[17][18][19][20]}

• Quinctia gens – Ancient Roman family