If you're bothered by the bad science inherent to the premise of Lucy - that old saw about how we only use 10% of our brain - strap in, because that's just the first step into insanity. The second is when the movie begins with a ludicrous-looking CGI ape-woman in primeval times (she will become the early human fossil also called Lucy, which is a thematic point). Rest assured, by the time Scarlett Johansson is explaining the meaning of life, the universe and everything [SPOILER: it's not 42], science and reason have long since ceased to be, and have become ex-science and ex-reason. To be blunt, this movie is incredibly dumb and also guilty fun - it's like inviting Nicolas Cage over to your house, getting him really wasted and then asking him to try and explain the origin of mankind. Not that I've ever done that. But I hope to...someday.
However, if I may echo the old truism about Marvel making a talking raccoon movie before DC does Wonder Woman, it's worth pointing out that Luc Besson just basically made a superhero movie with Scarlett Johansson as a woman powered by what may as well be Super Soldier serum, and Marvel still has no plans for a solo Black Widow movie. See how that works? If Rocket Raccoon were female, the conversation might be very different.
Lucy isn't specifically based on any one comic, but it borrows from a lot of them, most obviously Akira and Watchmen, without absorbing the intelligence of the source material. What Luc Besson is doing here reminds me of many evenings with my stoner roommate Greg from college, who once insisted he could see his own brain. And like every stoner I've ever known, Besson is a fan of nature-show footage, inserting clips of things like warthogs fucking and deer giving birth, in between lines of dialogue that explain how humans have such small perceptions of things, and everything's much deeper than that, man. But don't worry - there's plenty of shooting and stabbing and gruesome surgery and fast driving and telekinesis too.
Drunkenly hooking up in China with a dubious fellow in a cheap cowboy hat, Scarlett's Lucy is initially pretty dumb, but that doesn't merit the bad things which follow. Suckered into delivering a mystery suitcase to a crimelord (Oldboy's Choi Min-Sik) as part of a deal that's neither explained nor makes any sense, she soon finds herself with drugs surgically placed inside her stomach, forced to be a mule back to the U.S. Except before she can get to the airport, evil henchman take her to a rape room, because even in a female superhero movie, we're not allowed to be TOO progressive yet. Said henchmen, bizarrely, seem to not even be in on the plan, because they hit her in the stomach till the drugs burst, and then, presto...the drugs give her super powers.
Now, why they never gave anybody super powers before, or why nobody thinks to take them after this becomes clear, we'll never know. You'd think they'd fully test the product before smuggling it (in fact, they do test it super-briefly on a guy who looks like a meth-head, but he's hardly a good control subject). Anyway, Lucy soon becomes the equivalent of a walking organic Internet hotspot, able to hack not just electric things but organic ones too. Perhaps her greatest power, however, is to use a laptop computer on an airplane and somehow make it work online faster than any processor that actually exists.