why does elie lie to stein about his wife? was this action good?

Eliezer lies to the man, telling him that his family is doing well. Stein weeps with joy at the news. He continues to visit them for the next few weeks and occasionally brings them extra bread. He is thin and dried up, but he says that he is kept alive by the thought that his family is still alive. When a transport arrives from Antwerp, however, he discovers the truth about his family, and Eliezer never sees Stein again.