In the life cycle assessment (LCA) method, it is not possible to carry out an integrated sustainability analysis because the quantification of the biophysical capacity of the ecosystems to supply ecosystem services is not taken into account. This paper considers a methodological proposal connecting the flow demand of a process or system product from the technosphere and the feasibility of the ecosystem to supply based on the sink capacity. The ecosystem metabolism as an analytical framework and data from a case study of an LCA of combined heat and power (CHP) plant with and without post-combustion carbon capture (PCC) technology in Mexico were applied. Three scenarios, including water and energy depletion and climate change impact, are presented to show the types of results obtained when the process effect of operation is scaled to one year. The impact of the water–energy–carbon nexus over the natural infrastructure or ecological fund in LCA is analyzed. Further, the feasibility of the biomass energy with carbon capture and storage (BECCS) from this result for Mexico is discussed. On the supply side, in the three different scenarios, the CHP plant requires between 323.4 and 516 ha to supply the required oil as stock flow and 46–134 ha to supply the required freshwater. On the sink side, 52–5,096,511 ha is necessary to sequester the total CO₂ emissions. Overall, the CHP plant generates 1.9–28.8 MW/ha of electricity to fulfill its function. The CHP with PCC is the option with fewer ecosystem services required.