Two fundamental rules of good biblical scholarship will help us to understand a difficult scripture almost every time. First, look at the immediate context. Second, look at the broader context of the entire Bible. By contrast, attempting to understand a difficult passage by human reasoning is bad scholarship. Let's apply the proper rules systematically to the parable.
The immediate context (the verses before and after the parable) doesn't clearly provide us with further information, so let's go on to the second rule. Jesus said, "The Scripture cannot be broken" (John 10:35 John 10:35If he called them gods, to whom the word of God came, and the scripture cannot be broken;
American King James Version×). He meant that every section of the Bible on any given subject must be in agreement with every other section that addresses the same topic.
What does the Bible say about the state of the dead? A single phrase in Ecclesiastes 9:5 Ecclesiastes 9:5For the living know that they shall die: but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten.
American King James Version×summarizes the Bible's teaching about the state of the dead: "The dead know nothing." (See also Ezekiel 18:20 Ezekiel 18:20The soul that sins, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be on him, and the wickedness of the wicked shall be on him.
American King James Version×; 1 Corinthians 15:22-23 1 Corinthians 15:22-23  For as in Adam all die, even so in Christ shall all be made alive.  But every man in his own order: Christ the first fruits; afterward they that are Christ's at his coming.
American King James Version×, 51-52; John 3:13 John 3:13And no man has ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven.
American King James Version×, 16; Acts 2:29 Acts 2:29Men and brothers, let me freely speak to you of the patriarch David, that he is both dead and buried, and his sepulcher is with us to this day.
American King James Version×, 34; Romans 6:23 Romans 6:23For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
American King James Version×and many other passages that show that the soul can die, that physical death is like sleep and that the dead will be resurrected in the future, that no one has gone to heaven, that sin leads to death—not eternal life in another place, etc.).
Reading this parable to mean that the dead are conscious in an ever-burning hell or in heaven would be a clear contradiction with the broader context of the entire Bible. Indeed, it would be a misinterpretation.
However, we must understand that this is a parable—"an imaginary story…to illustrate and inculcate some higher spiritual truth" (International Standard Bible Encyclopedia, "parable"). If we take its lesson at face value, it is in complete harmony with the rest of the Bible. Jesus' straightforward point is that it is too late to change one's behavior and character after death. His point is that we must live in a godly manner when we are alive, just as the man Lazarus did in the story.
We bring together all of the scriptures about the afterlife in our booklets Heaven and Hell: What Does the Bible Really Teach? and What Happens After Death? They also contain further background information about this parable.