No unjust system is sustainable.
Sustainability is basically a system in which at least as much is given in as is taken out.
It is a society that satisfies its needs without jeopardizing the prospects of future generations. Without each of these, a system is not truly sustainable. If a society creates a system that is ecologically and economically viable but sacrifices the culture, then a major aspect of their lives has been eliminated, usually at great cost. A good example of this is many of the indigenous people of Central America and Mexico who have sacrificed their traditions to cater to a tourist economy. An ideal system would find a way to integrate cultural values and tradition into an economic livelihood.