Caesonius Lucillus was a member of the Arval Brethren, an prestigious priesthood of the time; Emperor Elagabalus is known to have been formally accepted as a member. He probably married a woman from the gens Ovinia, and together they had at least one child, Lucius Caesonius Ovinius Manlius Rufinianus Bassus, who was suffect consul twice.Mennen, pg. 92
