This study conducts a life cycle assessment and exergoenvironmental evaluation of a double-effect vapor absorption chiller (DEAC) with a cooling capacity of 352 kW, employing three different energy sources: natural gas, biomethane, and green hydrogen. The main objectives of this paper are as follows: (i) provide an exergoenvironmental model for DEAC technologies, (ii) evaluation of a case-study where a DEAC is used to cover the cooling demand of a specific university building in the Northeast of Brazil, and (iii) evaluate the scenario where the DEAC is fed by green hydrogen (GH2) and compare it with conventional energy resources (natural gas and biomethane). In order to develop the exergoenvironmental model, two methodologies are essential: a thermodynamic analysis and a Life Cycle Assessment (LCA). The thermodynamic analysis was carried out using the Engineering Equation Solver (EES: 10.998) software. The LCA has been developed through the open-source software openLCA version 1.10.3, with the Ecoinvent 3.7.1 life cycle inventory database, whereas the chosen life cycle inventory assessment (LCIA) method was the ReCiPe Endpoint LCA method (Humanitarian, medium weighting–H, A). The main results indicate that green hydrogen provides a 99.84% reduction in environmental impacts compared to natural gas during the operational phase, while biomethane reduces these impacts by 54.21% relative to natural gas. In the context of life cycle assessment (LCA), green hydrogen decreases fossil resource depletion by 18% and climate change-related emissions by 33.16% compared to natural gas. This study contributes to enhancing the understanding of the environmental and exergoenvironmental impacts of a double-effect vapor absorption chiller by varying the fuel usage during the operational phase.