The use of internet-based and networking technology in computer music systems has greatly increased in the past few years. Such efforts fall in the remits of the emerging filed of the Internet of Musical Things (IoMusT), the extension of the Internet of Things paradigm to the musical domain. Given the increasing importance of connected devices in the musical domain, it is essential to reflect on the relationship between such systems and sustainability at the environmental and social levels. In this paper, we address this aspect from two perspectives: 1) how to design IoMusT systems in a sustainable way, and 2) how IoMusT systems can support sustainability. To this end, we relied on three lenses, combining literature from green IoT (lens 1), Sustainable HCI (lens 2), and the Sustainable Development Goals from the United Nations (lens 3). By combining these three lenses, we developed five strategies for a sustainable IoMusT, which are extensively presented and discussed providing critical reflections.