The diversity of research on sustainable development shows that the analysis of the field of sustainable development is relevant and timely. Based on the paradigm of sustainable development, which states that it is necessary to live in such a way that the present resources are sufficient for future generations, the issues of social education for sustainable development are an important factor. The question arises whether there is even a single higher education institution at the non-university or university level in Lithuania today where sustainable development issues are not included in study programmes and separate courses related to sustainability are not taught. Various documents related to the Sustainable Development Goals (United Nations, 2015) and their implementation show that without an education system, without education, it is difficult to achieve sustainability. Therefore, the legitimate question arises whether higher educational institutions in Lithuania aspire to become “green” institutions, considering that these institutions are responsible for implementing the ideas of sustainability. The article aims to explore the situation of the Lithuanian HEI moving toward a green university. The research methods used include analysis of scientific literature and documents, content analysis, data processing. It can be assumed that in most Lithuanian higher education institutions, sustainability goals are integrated into the strategic plans and at the level of the institution as an organisation. However, the analysis showed that only a few Lithuanian universities are included in the green university rankings, and those do not reach the highest positions. Only a few universities and one non-university institution declare public information about the movement towards a green university. Only a few state non-university institutions in Lithuania declare social responsibility and provide publicly available social responsibility reports. Discussing the transition of higher education institutions from traditional to green institutions, it is useful to analyse the existing models or measurements of sustainability and the green university (HEI) paradigm. N.B. This article uses the terms non-university higher education institution and university as synonyms, especially when discussing a green university paradigm.