I can’t recall any verse of the Quran that says that people will lie on the day of judgement. To the contrary, there are many verses that state that on that day everything will be made so evident to everyone that they will not be able to deny anything. I’m copying one such passage below.
Quran 41:19-25
Translation by Asad
Hence, [warn all men of] the Day when the enemies of God shall be gathered together before the fire, and then shall be driven onward,till, when they come close to it, their hearing and their sight and their [very] skins will bear witness against them, speaking of what they were doing [on earth]. And they will ask their skins, “Why did you bear witness against us?” – [and] these will reply: “God, who gives speech to all things, has given speech to us [as well]: for He [it is who] has created you in the first instance – and unto Him you are [now] brought back. And you did not try to hide [your sins] lest your hearing or your sight or your skins bear witness against you: nay, but you thought that God did not know much of what you were doing – and that very thought which you thought about your Sustainer has brought you to perdition, and so now you find yourselves among the lost!” And then, [even] if they endure [their lot] in patience, the fire will still be their abode; and if they pray to be allowed to make amends, they will not be allowed to do so: for [when they became oblivious of Us,] We assigned to them [their own evil impulses as their] other selves, and these made appear goodly to them whatever lay open before them and whatever was beyond their ken. And so, the sentence [of doom] will have fallen due upon them together with the [other sinful] communities of invisible beings and humans that passed away before their time: verily, they [all] will indeed be lost!