Your assignment is asking for you to give your opinion about whether or not Elie's lie to his distant relative Stein was morally right. Consider the situation as described in Night and draw your own conclusion, based on how you interpret the events.
Elie and his father had been in Auschwitz for eight days when Stein found them and explained that he had no news about his wife and sons since he had been transported to the concentration camp two years earlier. Elie didn't know anything about the family but told Stein that they had received news and that all were well. Stein wept with relief and gratitude upon hearing the good news.
In the following days, Stein returned to visit, sometimes bringing bread for Elie to eat - probably from his own small ration. As he encouraged Elie to eat, he told them, "The only thing that keeps me alive...is to know that Reizel and the little ones are still alive. Were it not for them, I would give up."
When a transport arrives from his home town, he goes with certainty that someone in the group will have recent news about his family. Elie and his father "never saw him again. He had been given the news. The real news."
You must decide for yourself if it was morally right to give him hope by lying.
The question has to do with the "morality" of telling a falsehood. In this case I would argue that context is everything. In the camps, concepts like "truth" and "morality" are transformed. Stein has no information about his wife, nor is he likely to ever get any. For him, the "truth" about her, as we conventionally understand it, is simply unavailable. However, it is absolutely true that his need to know about his family is emotionally imperative. As he says, knowing they are alive "is the only thing that keeps me alive."
In another famous book on the Holocaust, Victor Frankl writes in Man's Search for Meaning about how the image of his wife became real for him; though they were separated, and though he knew nothing about her fate, the idea of her kept him alive. Stein is the same way. More than the physical privations of the camp, the truly deadly thing about the camps was the loss of hope. To me, Eliezer's "lie" was a way of providing that hope. If he had told the truth and removed all hope, that would have killed Stein as surely as a bullet.