Remember that Eliezer and his father were sent off to Auschwitz, which as commonly known today is a death camp. To determine whether they go to Auschwitz or Birkenau (the labor camp next to Auschwitz), they were asked for some of the following things:
1) Age
2) Occupancy
3) Health condition
4) (i believe there might be more) etc.
Each of these determine if they can work, and depending on what they answer, they were either sent directly to the death camp, or were sent to the labor camp.
Now, to answer the question, they were told to lie about their ages so that they would have a higher survivability rate.
hope this helps
