Lucy achieves 100% brain function and disappears into the space-time continuum.  Jang is killed by Del Rio.  Professor Norman and his colleagues receive a large flash drive from Lucy's supercomputer, which contains all of the knowledge she has learned.

Lucy Miller (Scarlett Johansson) is an American studying in Taipei, Taiwan.  Her new boyfriend Richard has given her a briefcase and asks her to deliver it to Mr. Jang (Choi Min-sik), a Korean mob boss and drug lord, at a hotel.  She is scared and doesn't want to do it, but Richard handcuffs her to the briefcase and makes her do it.  As she enters the hotel, Richard is killed and she is taken by Jang's henchmen.  In Jang's hotel room, Lucy is forced to open the briefcase, and inside it are four bags of blue crystals that is actually a synthetic drug called CPH4.  Jang orders his men to take one of the bags and sew it inside her, and she and three others will be used as drug mules to transport the CPH4 into Europe.  While recovering from the surgery, one of her captors repeatedly kicks her in the stomach, breaking open the bag and releasing the drug into her system.  Instantly, the formerly scared girl becomes a confident woman, and she quickly dispatches her captors, takes one of their guns, and escapes.

Lucy goes to a local hospital and has one of the doctors remove the bag.  After she tells him what it is, the doctor tells her that CPH4 is a substance generated by pregnant women that is used in fetal development, and it has dangerous side effects.  Lucy takes the bag of drugs and then returns to the hotel.  After killing Jang's bodyguards, Lucy gets the location of the other three mules by forcibly mind-melding with Jang.  She then goes to her apartment, gets on her roommate's laptop, and begins to download everything she can find about brain function.  It's at this time she learns about Professor Samuel Norman (Morgan Freeman) and his theories about what happens to the human brain if it can utilize more than the 10% an average person uses.  She then contacts Professor Norman, and she tells him that his theories are correct.  After demonstrating to him that she really is currently using way more than 10% of her brain, and he tells her that she should pass along everything she has and will learn during this experience, they decide to meet at his lab in Paris the next day.

After hanging up with Professor Norman, Lucy calls the Paris Police, and tells Detective Pierre Del Rio (Amr Waked) about the other drug mules, because one of them is also going to Paris (the others are going to Berlin and Rome).  Del Rio coordinates with the Berlin and Rome police and they apprehend the mules and are extradited to Paris.  On her flight to Paris, Lucy's body begins to disintegrate.  She has to take more of the CPH4 to re-stabilize her cells (and passes out as a result), but it also accelerates the growth of her brain function.  Throughout the movie, we see a full screen of a percentage showing how much brain function Lucy has at that time (currently at 40%).  As her function increases, her capabilities increase as well.  In addition to communicating telepathically (like she did to Jang), Lucy has heightened senses, can control matter, and see things on a molecular level.

Lucy wakes up in a Paris hospital, where Del Rio and other detectives are waiting for her.  They attempt to arrest her, but she knocks them out with a wave of her hand, except for Del Rio.  She tells him that Jang and his men are also coming to Paris to get the CPH4 for themselves, and she needs him to get the drugs from the other mules to her so she can continue her "research".  Jang's men are already at the hospital, and they kill the mules and the cops watching over them so they can retrieve the bags of CPH4.  Lucy is able to incapacitate them and get the drugs for herself, then she and Del Rio race through the streets of Paris to get to Professor Norman's lab before Jang and the rest of his men can catch her.  Now at the lab, Lucy proceeds to tell Professor Norman and his associates everything she has learned about what happens as one's brain function increases.  Since her knowledge is way more than any human can possibly comprehend, she has the other professors turn the remaining bags of CPH4 into an intravenous liquid so she can inject it into herself.  With her brain function approaching 90%, Lucy begins to metamorphose into a supercomputer so she can download all of her knowledge into it.

Meanwhile, Del Rio and other Paris policemen are trying to hold off Jang and his henchmen outside of the lab.  One of them uses a rocket launcher to blow open the door, which causes Lucy to be blasted out of the room, all the way to Times Square in New York.  There, she is able to time-travel back to prehistoric times, where she meets early man.  She touches fingers with him, which sends Lucy into the cosmos and back in time to the creation of the universe, giving her unlimited powers.  With her function at 99%, Jang enters the lab and prepares to shoot Lucy (her physical body never left the lab).  Just as he pulls the trigger, Lucy's brain achieves 100% functionality and she disappears into the space-time continuum.  Del Rio then enters the lab and kills Jang.  He then asks the professors where Lucy went, but then his cell phone beeps.  He received a text message from Lucy, telling him that she is everywhere.

The movie ends with Lucy's supercomputer creating a large flash drive, which contains all of the knowledge Lucy has learned.  After Professor Norman takes it, the supercomputer disintegrates, all all physical traces of Lucy are gone.

Thanks Steve!