Actually were two writers with similar names. There was a Roman satirist named Lucilius and a Greek poet named Loukillios (Greek Λουκίλλιος, Latinized as Lucillius).
For Lucilius see:
http://www.ancientlibrary.com/smith-bio/1931.html
For Lucillius see:
http://www.ancientlibrary.com/smith-bio/1933.html
I can't find an etymology for the name, but I am wondering if it isn't related to Loukas based on its Greek form. Loukas is from Lucania which ultimately seems to have a debated meaning as highlighted here:
http://incomingbasilicata.wordpress.com/2009/02/10/basilicata-or-lucania/
and this page (in Italian):
http://archiviostorico.corriere.it/1996/luglio/03/Russia_trovera_nuovo_padrone_co_0_9607033254.shtml