Most of what I've heard about Lucy is negative. The film was criticised for just about everything, from direction to acting to script, or at least that's how it seemed. It was also heavily criticised for, once again, relying on a fallacy of modern "science": that we only use 10% of our brain on average.
For that last part it definitely deserves criticism. That "statistic" is pseudo-science nonsense that refuses to die, no matter how many people point it out as such. That said, as far as the premise goes, at least Lucy ran with it in some interesting directions. Having thrown science out the window to grant it a core concept you can't really categorise the film as sci-fi, but as fantasy it is a little more interesting. The usual tropes all appear, from metabolism control to Jean-Grey like psychic abilities, but are interspersed with some more unique ideas. The visualisation of data streams, both within plants and the global mobile networks, were interesting (if, again, not particularly accurate) and her driving sequence was damned effective with some clever visual direction on display.
Fun effects aside, Lucy also behaves in a nicely rational manner. It seems that whenever people "unlock" the power of their brain in films they are overtaken by relatively basal desires: greed, lust or revenge are all common. Lucy, on the other hand, actually seems to get an IQ boost, determining that she hasn't long to live and that the best use of her remaining life is to continue the experiment in a scientific environment. Here, at least, Lucy deserves a thumbs up for portraying genuinely intelligent behaviour. Even if the end result is that she becomes some kind of transcendent computer/god hybrid.
The usual problems with an all-powerful antagonist are also present. At any time Lucy could just wave a hand and kill her opponents. In fact, she stands in front of her main adversary and doesn't kill him, for reasons that remain unexplained. Here her intelligence should be questioned, as countless people end up dying for her to complete her experiment when her help would take nanoseconds. The result is that most of the action sequences in the latter half of the film feel dumb. It doesn't matter how much you dress them up or write Lucy off as having to concentrate, they just don't make any sense.
Overall, Lucy is a fun enough watch but suffers from a silly core premise. Much like the acting or direction, the film is largely fine, but nothing here is going to blow you away or leave much of an impact.