Territorial LCA (T-LCA) allows to carry out an environmental assessment of all production and consumption activities within a given territory, however without considering an absolute sustainability perspective. This paper aimed to apply the AESA framework in a T-LCA approach to discuss its feasibility and usefulness. The example of La Reunion Island, a French region in the Indian Ocean, was used as a case study. A T-LCA of La Reunion was conducted using customs data on imports and exports of all goods traded in 2021 to establish an environmental baseline. Applying the AESA framework to this case required addressing two key methodological aspects, sharing principles (SPs) and AESA metrics. Several SPs aligned with the 'earth system justice' framework were applied, considering both territorial multifunctionality (e.g., residential, economic, social) and impact location (in- site and off-site impacts), in order to offer complete insights for political and economic stakeholders. Two main approaches can quantify absolute environmental sustainability, based on i) life cycle impact assessment (LCIA) methods, or ii) planetary boundary (PB) framework. Both were used to assess their main differences in terms of modelling assumptions and result interpretations, focusing on four PBs (climate change (CC), freshwater (FU) and land use (LU), and biogeochemical cycles (BCs)) to address global and local issues. Results were sensitive to the SP applied. FU, LU, and BCs results have varied around thresholds, while those of CC were always above. Results also highlighted that the chosen AESA metric affected results, e.g. nitrogen compound impacts were near the threshold using the LCIA-based metric but significantly exceeded it with the PB-based metric. This application of the AESA framework to T-LCA laid the methodological basis for a T- AESA by proposing SPs and comparing metrics. It also revealed the need for methodological developments to territorialize carrying capacities and AESA m