Lucius Fox was an employee, and later CEO, of Wayne Enterprises. He worked in the R&D department, which was just a place he was put to keep him out of the way.
Batman Begins Edit
After Bruce Wayne's return to Gotham, he visited the R&D department and met Lucius. He asked if he could see the equipment Wayne Enterprises had made, claiming he was using them for base jumping and spelunking. Fox provided him with a Nomec survival suit, a cape of memory fabric, and a utility belt. He also gave him The Tumbler, a high powered military vehicle. He told Bruce that he knew he wasn't using these items for pleasure, but he agreed not to ask any questions.
Later Lucius was called by Alfred Pennyworth after Bruce was infected with fear toxin. Lucius made an antidote, which saved Bruce's life. William Earle then visited Fox and told him that a microwave emitter had gone missing, which could be used to vapourise the water supply of Gotham. Earle then fired Fox. After attending Bruce's birthday party a little later, Fox was asked to make more of the antidote. He broke into Wayne Enterprises to do so, and made enough to treat the infected of Gotham who had been hit by the infected water. Later Wayne bought the majority of the shares of Wayne Enterprises and installed Fox as the CEO.
The Dark Knight Edit
Fox then ran Wayne Enterprises, presenting an investment opportunity from Mr Lau. Bruce Wayne fell asleep at the meeting, and Coleman Reese brought his concerns to Fox, who dismissed them. Lucius also designed a new suit for Batman. Bruce told Fox that Lau was in business with the mob, so sent Lucius to Hong Kong, ostensibly to turn down the offer in person. He actually planted a phone in Lau's building which used ultrasound to map out a schematic of the place, so Batman could break in and capture Lau. He used Fox's "sky hook" technology to extract himself safely.
Later Fox was confronted by Reese again, who claimed to know Batman's identity was Bruce Wayne. Fox dismissed this again, but Coleman Reese went public with the claim. Fox noticed a break in at R&D, and found Bruce Wayne had broken in to install a computer that would map out the entire city using everyone's cell phones. Lucius disagreed with the ethics of invading everyone's privacy, and told Bruce Wayne that he wanted nothing more to do with him after using the computer. After he helped Batman defeat the Joker using the technology, Lucius then entered his name as instructed and watched as the machine destroyed itself. His faith was rewarded by Wayne.