How does the quote"Lennie, for God's sakes don't drink so much" related to the Great Depression?

This is an interesting question.  George and Lennie's interaction in this scene does offer insights about the Great Depression in two ways. 

First, the men are poor.  They have little to eat and little to drink.  Many people during the Great Depression lost their jobs and so they could not take care of themselves well. We can see this clearly in this scene.  George and Lennie had to drink from a stagnant body of water, even if the water might make them sick.  George actually mentions that Lennie got sick the day before. 

Second, George and Lennie are migrant workers, who have left one place of employment, and they are sojourning to another.  They know nothing of settling down.  They are in this predicament, because during the depression, jobs were scarce, and men had to go wherever they could find work.