Lucy ends up drugged after a beat of one of the captors, and from this point on, the film becomes very interesting because the drug increases the brain capacity progressively from 10% - the average of humans - to 100%. Meanwhile, another character is presented. Morgan Freeman becomes a Professor, named Norman, that is working on a theory where he wants to discover what could happen if a human could use more brain capacity than the average.
If the film would have centered the attention in the Johansson's and Freeman's characters, it could have been - as said previously- a really good film, with a cleverer screenplay, because it contain some really good scenes where they talk about the brain and how the brain capacity affects a human but Besson shuns this and centers a lot of attention into the persecution of the corean dealers to recuperate the drugs and the kill Lucy.
In conclusion, seems like Luc Besson wanted to do an action film where the heroine is very different from the DC or Marvel comics, and from the typical films of this genre. The strong points of this film are the main idea, the performances of Johansson and Freeman. However, the weak ones are the fact there's a lot of action in a 90 minute film that should have been longer to explore a little bit more the great idea of having a more brain capacity than the average.