An increasing number of studies apply life-cycle assessment methodology to assess the impact of a new building or to prioritize between different building refurbishment strategies. Among the different hypotheses to consider during the application of this methodology, the selection of the impact indicator is critical, as this choice will completely change the interpretation of the results. This article proposes applying four indicators that allow analysing the results of a refurbishment project of a residential building with the life-cycle approach: non-renewable primary energy use reduction (NRPER), net energy ratio (NER), internal rate of return (IRR), and life-cycle payback (LC-PB). The combination of environmental and economic indicators when evaluating the results has allowed to prioritize among the different strategies defined for this case study. Furthermore, an extensive sensitivity assessment reflects the high uncertainty of some of the parameters and their high influence on the final results. To this end, new hypotheses related to the following parameters have been considered: reference service life of the building, estimated service life of material, operational energy use, conversion factor, energy price, and inflation rate. The results show that the NRPE use reduction value could vary up to −44%. The variation of the other indicators is also very relevant, reaching variation rates such as 100% in the NER, 450% in the IRR, and 300% in the LC-PB. Finally, the results allow to define the type of input or hypothesis that influences each indicator the most, which is relevant when calibrating the prioritization process for the refurbishment strategy.