Lulier was born and died in Rome. He was a student of Pietro Simone Agostini, a composer and violin virtuoso in the service of Pietro Ottoboni. From 1676 to 1699 Lulier played regularly in the Roman church of San Luigi dei Francesi; on 13 October 1679 he entered the Congregazione di Santa Cecilia. From 1681 he was active in the service of Benedetto Pamphili and from 1688 he played the trombone in the Musici del Campidoglio. When Pamphili left Rome in 1690, Lulier again became the protégé of cardinal Ottoboni and remained so for the rest of his life. In the 1690s he also worked for the Borghese family, and probably played the cello in the orchestra in which another Pamphili protégé, Arcangelo Corelli, was principal violinist.
No instrumental works for cello by Lulier have survived, but a number of vocal works with concertate cello parts do. His compositions include cantatas and a number of oratorios.