Lucius Cornelius Sulla was a Roman senator of the Augustan age. He was ordinary consul as the colleague of Augustus in 5 BC.Alison E. Cooley, The Cambridge Manual of Latin Epigraphy (Cambridge: University Press, 2012), p. 458 The only other office attested for him was as a member of the Septemviri epulonum, which he was co-opted into after his praetorship. = ILS 920
Ronald Syme believed he was a son of Publius Cornelius Sulla, designated consul for 65 BC, which made him a grandnephew of the Roman dictator Lucius Cornelius Sulla.Syme, The Augustan Aristocracy (Oxford: Clarendon Press, 1986), p. 86 The son of Lucius, Cornelius Sulla, was expelled from the Senate by Tiberius in AD 17.Tacitus, Annales, ii.48
References
Further reading Werner Eck, "Cornelius [II 58]" in Brill's New Pauly (online edition). Prosopographia Imperii Romani (PIR2) C 1460