Lucy was not a good movie. It tries far too hard to appear as though it is profound and insightful, but ultimately all the effects, dialog, and pittance that they called a plot were only there to hide the fact that the movie had nothing valuable to say.
The only real positive thing I have to say about the movie is that before Lucy gained her "super powered brain", Scarlett Johansen's performance was really good. I felt the character's fear, and was genuinely concerned for her. After she takes the drugs though, her character apparently becomes an uninteresting and emotionless robot. The rest of the film follows suit.
The biggest reason Lucy fails is because it tried too be Hard Science-Fiction and did it poorly. The movie could have skipped all of the lectures by Morgan Freeman (though, then the movie would've had no Morgan Freeman) and simply said it was an untested drug. People can accept that. Fine. Drugs don't typically do that kind of stuff, but who knows. It could happen. But once they tried to explain what was happening in great detail, using "science", they upped the ante.
Science Fiction by-in-large starts in logical and scientific and works its way out. Soft Science Fiction can get away with more because it doesn't have to explain as much. Transformers could be considered "Soft Science Fiction" because the movies never explain in detail how the transformers actually transform. It is based on the fact that alien life could very well be out there, alien technology could be anything (if it exists) and the way the Transformers transform involves mechanical rearrangement of parts that we can see. So, sure, its possible (though impractical).
When Science Fiction is Hard, it is held to a higher degree of scrutiny and accountability. It tries to sell the audience on what happens by explaining it with existing science and then, following the rules of science and logic, extends what is known into what is feasible but ultimately fictional. For instance, Rise of the Planet of the Apes is Hard Science Fiction. The science sounds realistic in the movie.
Planet of the Apes Spoilers: "In Planet of the Apes, scientists are developing a drug to try to cure alzheimer's which has to do with brain function. In both Humans and Apes it has very positive effects on their mental capacity. We know drugs have been shown to be able to alter the mental state, memory, cognition, etc. So this is believable. They use a virus to deliver the medication, which is also something based on real science. Still believable. They use an aerosol delivery method, still plausible since we know many microorganisms can transmit between creatures via air. They strengthen the treatment to make it more aggressive. Human beings can't handle it the same way Apes can. We know many illnesses affect different species differently, so this checks out. So is a medicine that makes Apes have human-level intelligence believable? Yes. Could it actually happen? It seems unlikely, but it is still possible.
Now consider Lucy. The movie claims we only use 10% of our brains. Nope. That claim is grossly untrue. The movie claims we can control other people simply by unlocking more of our "brain power". Okay, we could maybe accept this, but how? You can't just "unlock more brain" and then defy the laws of the universe. Brains, as we know them, only have the ability to store memories and control our bodies using our nervous system. Since the movie went to great lengths to describe the whole 10% thing and try to make it scientific, it can't just gloss over major issues like this. We know brains don't contain microwave emitters or any other similar nonsense.
If the movie wanted to make this plausible, they could have said something like: our brains can control other people at over 10% utilization because the brain starts emitting electromagnetic waves (which is what electrical impulses between synapses fundamentally are), or maybe there is an invisible substance in the air that can be manipulated by thoughts... Say something. But the movie doesn't. Instead it just keeps on heaping on faulty claims and reasoning, while glossing over important bits. This problem is ever-more exaserbated as they keep heaping on the 10% garbage. We know this isn't true. We know we use 100% of our brains. The movie's plausibilty rests on premise that we don't use our whole brain, and that premise is false. The more time they spend trying to defend this false claim, the more implausible the whole movie becomes.
Even if we were to accept this 10% thing as somehow believable, the way it is built up thereafter doesn't make any sense. Could unlocking more of your brain make you capable of consciously regulating your metabolism? Sure. The brain has influence over its own metabolism now but its just an involuntary process, so that's believable. Could it make you "smarter"? Definitely, though smarter is such a nebulous concept. Could it make you think faster? Yes. Perhaps with added control over metabolism and other unconscious body functions you could heal faster or perform super-human gymnastics. But does having more access to your brain suddenly render the forces of the universe that hold your cells together invalid? It certainly does not.
At one point in the movie Lucy is on a plane and her cells start trying to "escape" her body. Not only does this incident make no sense scientifically, but it also goes against the movie's own claims! According to the movie, she is supposed to now have more control over her body. Her brain is apparently now so powerful she has the ability to control not just her own body, but other people, and other matter. When her cells were bursting apart she was not in any sort of strained mental state at the time. She was not being overwhelmed or exhausted. Why would she suddenly start dissolving now of all times? If I had to guess, I would say that whole scene was all about the visual effects and had nothing to do with plot.
Let's also not confuse capability with knowledge. Knowledge has to be gathered and learned, it can't just "happen" yet Lucy immediately picks up languages and all sorts of knowledge she wouldn't already have. Could she learn faster and understand more? Sure. Should she have immediately known all these things? Absolutely not. Knowledge doesn't simply exist in the ether, and if the movie wanted to claim that knowledge does exist in that way, it should have stated it.
If the movie's claim of only using 10% of our brains is to be believed, there is also no way she should have had all that intricate knowledge of her past stored up in her head. Before the other 90% was unlocked, she didn't have those memories, then when it was unlocked, she had them. That would suggest that she was using some of that other 90% all along in order to pick up the details the 10% didn't pick up, which challenges the premise for the movie yet again.
Finally, the movie relied waaay too much on actions that appeared intelligent, but were ultimately hollow. For instance, when Lucy is on the airplane she is typing into two laptops at once, because she's just so smart and fast now, but... What on earth is she typing up? Nothing comprehensible is appearing on the screen, and at no point in the movie is there any apparent result of this. She wasn't doing research. She doesn't need a computer in order to "hack" into other devices, as we saw earlier in the film. She wasn't writing anything down. Its safe to say she wasn't doing anything. Which sums up the movie pretty nicely. It tried really hard to look and sound smart, but in the end, it was meaningless.