Is the life lesson to listen to your elders?

Yes, to a certain degree. At the beginning of The Devil's Arithmetic, before she is taken back in time, it is made very clear that young Hannah does not understand what her older family members went through as Jews during the Holocaust. She is embarrassed by their behavior, especially her Grandfather's, and wishes that they would forget the past.
When Hannah returns to the present after her journey through the past, having lived as a prisoner in a concentration camp, she now fully and completely understands why her family cannot forget and does not want to forget the Holocaust.
So yes, one could interpret the "life lesson" of The Devil's Arithmetic to be "listen to your elders," but I believe this lesson works in combination with another: Don't judge a man until you've walked a mile in his shoes. As a child who had never before known what it meant to suffer, Hannah found it easy to judge her family and be embarrassed by them. When she suffered as they had, Hannah knew that she had been wrong to feel this way, and cherishes her family in a way that probably would not have been possible beforehand.