Yes, it is discredited. In fact, I used to play the trailer for Lucy in one of my lectures just to discuss how wrong it is.Lucy (2014) Peacock Network
Fun sci fi action movie based upon I thought discredited concept that humans use only 5% of our brain
Where it comes from is unclear. Possibly it's that the brain consists of two types of cells, neurones and glia. Glia conventionally were not believed to be involved in brain communication (this is now an issue of controversy, where I favour the theory that they do contribute), and that they were once thought to be about 90% of brain cells - this has since been revised to around 50%. Although there are other theories. Human brains have a lot of "spare" neurones - we start with far more than we need and they gradually die off (I think about 0.5-1% a year) throughout our lifespan because of a "use it or lose it" basis of survival. However, this doesn't mean the "spares" are not doing anything at all, or that there's some way to drag them into action.
Anyway, you can assume your brain is working to capacity. I would argue that some people have brains that occasionally operate beyond normal capacity, and the medical term for that is "epilepsy". The sort of activity Lucy's brain would have (according to the film) would require massive cellular energy requirements far beyond the brain's metabolic ability to support, so she'd really just keep collapsing into unconsciousness, plus almost certainly experiencing progressive brain damage. I accept, however, that would be far less fun as a film.