Aulus Bucius Lappius Maximus was a Roman senator who flourished during the Flavian dynasty; Brian W. Jones considers him one of Domitian's amici or advisors. He held the consulate twice. He is primarily known through inscriptions.
The polyonymy of his name indicates an adoption; according to Olli Salomies, he was born a Lappius Maximus adopted by an Aulus Bucius. Salomies also notes that "all A. Lappii seem to have something to do with the senator".
The career of Lappius Maximus included being proconsular governor of Bithynia et Pontus during 83/84 prior to being consul for the first time for the nundinium September–December 86 with Gaius Octavius Tidius Tossianus Lucius Javolenus Priscus as his colleague. Then he was consular legate of Germania Inferior during 87 to 89, during which time he assisted in crushing the revolt of Lucius Antonius Saturninus in the adjacent province of Germania Superior. Afterwards he was immediately assigned to the consular legateship of Syria from 89 to 92, before holding the fasces a second time for the nundinium May–August 95 with Publius Ducenius Verus as his colleague.
Salomies writes that Lappia A.f. Tertulla, mentioned in a Roman inscription (CIL VI, 31106) "is probably this man's daughter".