How can it be a lie when no one knows exactly if animals have an afterlife? The Bible didn't say much about their fate, but they have a value in God's eyes. Perhaps we need not know what becomes of them since we (who are created in the image of God) has to worry and focus about our own salvation. The Bible is focused on the salvation of Man.
However, we are likened to animals:
Ecclesiastes 3:18
18 I said in my heart, “Concerning the condition of the sons of men, God tests them, that they may see that they themselves are like animals.”
The result of earthly death is the same for man and animals. Equal in death.
Ecclesiastes 3
19 For what happens to the sons of men also happens to animals; one thing befalls them: as one dies, so dies the other. Surely, they all have one breath; man has no advantage over animals, for all is vanity. 20 All go to one place: all are from the dust, and all return to dust.
As the verse by Solomon indicate, animals have spirit. Therefore, we cannot say for certain that there is no doggie "heaven,"
Ecclesiastes 3
21 Who knows the spirit of the sons of men, which goes upward, and the spirit of the animal, which goes down to the earth?