How does the idea of "sustainability" square with the fact that developing countries must usually draw heavily on their natural resource base?
In order to develop economically, they usually have to do this.
There are many possible ways to answer this question. You should probably check to be sure that there is not one particular answer that your text or teacher has given that you are supposed to provide.
One way to square these ideas is by understanding that an economy that depends on natural resources does not need to be unsustainable. It is often possible to use technology to reduce the amount of natural resources that is needed to produce goods and services. For example, more fuel-efficient trucks reduce the need for energy in transporting goods.
Another way to square these ideas is to understand that a developing nation's economy does not have to continue to rely on resources. As the economy develops it can move on into less resource-intensive activities. This allows the country to move away from unsustainable activities.