Lucius Fox is Bruce Wayne's business manager. He also helps Batman design his gadgetry, in particular the Grapnel Boost.
He was responsible for designing the security system in Arkham Asylum. The results were good enough that both Batman and Oracle were unable to hack them, with Oracle sardonically remarking that "Lucius did a good job".[1]
Once he grew tired of his relatively slow movement in Arkham City, Batman chose to ignore Fox's warnings about the boost not being ready for deployment, and used it navigate the prison much faster. Fortunately, the device functioned perfectly, and showed no negative repercussions.[2]
Later, when Batman had been given a post-hypnotic suggestion by Mad Hatter, Batman believed that Fox had managed to create a cure for the Titan illness that had afflicted him. However, this was merely a trap.[2]