It’s not a lie. Christ hung on the cross for all of our sins, not just those who accept him. In order to take advantage His Atonement, one must repent of their sins, acknowledge Christ as their Savior. For those who do not repent, they shall suffer for their own sins. But there will be an end to that suffering and then everyone will receive their reward, according to their worthiness, and the desires of their hearts. Yes, I really do believe this.
There is a book of life, and then their is the book in which are recorded your works/deeds in life. In Rev 20 we see that the life book is opened and ‘the books’ of the works of those standing for judgment. Because those trusting in Christ are Saved by faith, not by their works. Please follow the essentials. Would you rather be judged according to what works are in your book, or redeemed by the Blood of the Lamb slain from the foudation of the world? Do believe they are equate-able, your works and His redeeming Blood?
Two bad assumptions here: The first one is that "resurrection" is always a "good thing" (LDS believes that the atonement basically provides a resurrected body for all). You say "receive their reward," well look at this reward of resurrection: Read John 5:29: "they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation."
Ya see? Joe Smith didn't bother to read the revelation of John 5 very closely. He thought he could just redefine "damnation" to "dam" like a river (oh sure, that's why folks think of a lake everytime you say "oh, damn it!") The problem is that in LDS thinking, damnation occurs prior to the resurrection...and so when they are confronted with the reality of a "resurrection of damnation," it's back to the spiritual drawing board.
The second bad assumption is to redefine all of the "everlasting" and "eternal" words in the Bible, Book of Mormon & D&C to mean less than "everlasting" and "eternal" when it comes to describing "hell" but then to twist it back to its normal meaning when describing heaven & the kingdom of God. And many scriptures make it plain that hell is the spirit prison; there's nothing temporary about the place OR the condition.