The livestock sector has complex relationships with the three fundamental pillars of sustainability, i.e., environmental, economic, and social. Devising a livestock farming strategy by considering the different sustainability pillars is essential. Although several decision support systems (DSSs) are available for the livestock sector, these DSSs differ in the way they address sustainability. This work emphasizes the importance of a holistic approach to sustainable livestock management rather than only targeting individual sustainability dimensions. We, therefore, propose an initial assessment framework to evaluate the capacity of livestock DSSs in targeting the different sustainability pillars. In line with this, we present a conceptual basis for deriving assessment criteria and indicators. We then use the proposed assessment framework to assess existing openly available livestock DSSs. We observe that the main focus of the existing and openly available livestock-related DSSs is on the indicators from environmental pillars, and only a few of them accommodate economic aspects. No openly available DSS includes social and governance-related points. More importantly, none of these DSSs can handle data streams from Internet of Things (IoT) devices and, hence, they miss on the superiority that advanced modelling techniques can provide. With these observations, we draft an extensive set of guidelines for future livestock-related DSSs to holistically target sustainability.