In addition to what the others have said there are numerous other passages and oddities that hint at Quirrel = Voldemort = Harry's dark side. Harry and Quirrel describing a Horcrux between them when they talk about the Pioneer plate. Quirrel saying he "resolved his parental issues to his satisfaction" long ago, just after saying being grateful for his parents could never have occured to him. Quirrel having a much better model of Harry than of Draco or Hermione, particularly when Harry's dark side is involved. Harry's dark side and Quirrel both being extremely vulnerable to Dementors. Harry's dark side and Quirrel both being very good at pretending to be other people. Quirrel's extremely odd reaction when Harry talks about having a mysterious dark side and his going along with the convenient conclusion that it's just another part of Harry. Dumbledore and Snape recognizing Voldemort's hand in Quirrels actions. Harry's dark side hating Dumbledore. And so on.

The strongest piece of evidence for Lucius believing Harry to be Voldemort is his "I know it was you" message after breaking out Bellatrix.