Anyone can die for a lie. We don't need to dig too far for an example. But I would be willing to stake my own life on the belief that no one would willingly die for something they knew they had made up. In fact, a lot of people won't even be willing to die for what they believe is the truth.
Why, then, did the Apostles unanimously testify, even under threat of death, that they had seen the risen Lord? To give a comparable scenario, there is another religion that bases its claims on the testimony of witnesses. The beginning of the Book of Mormon contains two signed testimonies, one by three witnesses, one by 8. Yet, consider the following quote from Mormonism's second prophet, Brigham Young: "Some of the Witnesses of the Book of Mormon, who handled the plates and conversed with the angels of God, were afterwards left to doubt and to disbelieve that they had ever seen an angel." (1) I have even heard it said that by 1847, a mere 17 years after the publication of the Book of Mormon's first edition, not a single witness was still associated with the Mormon Church. Can you imagine such weak faith from Peter or Paul, or even from John, the only Apostle to die a natural death?
So the question remains: why were the Apostles so willing to die? Why would the men who fled when soldiers arrested Jesus die for the claim that He was alive? Why would Peter, who denied three times in a night that he even knew who Jesus was, give his life for the claim that He had risen? Why would Paul, the Jewish equivalent of an ISIS militant, make the ultimate sacrifice for a God he spent a long time persecuting? The obvious answer is that they all believed!
That leaves us with another question. Why did they believe? Is it possible that these devout Christian martyrs endured a torturous existence because they had genuinely seen the risen Lord? Such a conclusion makes more sense than any claim of mischief or delusion.
References
1. Young, Brigham - Journal of Discourses, Vol 7, 1859