Systematic Literature Reviews (SLRs) are a widely employed research method in software engineering. However, there are several problems with SLRs, including the enormous time and effort to conduct them and the lack of obvious impacts of SLR results on software engineering practices and industry projects. To address these problems, the concepts of \textit{sustainability} and \textit{sustainable SLR} have been proposed, aiming to raise awareness among researchers about the importance of dealing with SLR problems in a consistent way; however, practical and concrete actions are still lacking. This paper presents concrete directions towards sustainable SLRs. We first identified 18 ``green drivers'' (GD) that could directly impact SLR sustainability, and we distilled 25 sustainability indicators (SI) associated with the GD to assess SLRs regarding their sustainability. A preliminary evaluation was conducted on the ten top-cited SLRs in software engineering published over the last decade. From this analysis, we synthesized our insights into 12 leverage points for sustainability. Our results indicate that even in high-quality reviews, there are threats to sustainability, such as: flaws in the search process, lack of essential details in the documentation, weak collaboration with stakeholders, poor knowledge management, lack of use of supporting tools, and a dearth of practical insights for software engineering practitioners. The good news is that moving towards sustainable SLRs only requires some simple actions, which can pave the way for a profound change in the software engineering community's mindset about how to create and sustain SLRs.