The statement that humans only use 10% of their brain is a common urban myth that scientists of that caliber would have known. It refers to unused potential. In fact, brain scans have shown that no matter what you are doing all parts of the brain are active, though some are more active than others--which is explained in this movie by Niko.
The name "Zoe" is the Greek word for life.
The potato chips in the film are the fictional Let's Potato Chips, which are also found in the TV show Community (2009), starring Donald Glover.
Olivia Wilde stated in an interview that her character was inspired by John Malkovich's character, Vicomte Sebastien de Valmont from the film, Les Liaisons dangereuses (1988).
The title comes from a Bible story in the Gospel of John, in the New Testament. Lazarus was a man who was resurrected by Jesus after being dead for four days. In fact, the penultimate frame of the trailer for the movie gives the Scripture reference: John 11.