The problem of power grid capacity expansion focuses on adding or modernizing generation and transmission resources to respond to the rise in demand over a long-term planning period. Traditionally, the problem has been mainly viewed from technical and financial perspectives. However, with the rise in the frequency and severity of natural disasters and their dire impacts on society, it is paramount to consider the problem from a nexus of resilience, sustainability, and equity. This paper presents a novel multi-objective optimization framework to perform power grid capacity planning, while balancing the cost of operation and expansion with the life cycle impacts of various technologies. Further, to ensure equity in grid resilience, a social vulnerability metric is used to weigh the energy not served based on the capabilities (or lack thereof) of communities affected by long-duration power outages. A case study is developed for part of the bulk power system in the state of Colorado. The findings of the study show that, by considering life cycle impacts alongside cost, grid expansion solutions move towards greener alternatives because the benefits of decommissioning fossil-fuel-based generation outweigh the costs associated with deploying new generation resources. Furthermore, an equity-based approach ensures that socially vulnerable populations are less impacted by disaster-induced, long-duration power outages.