Buildings account for 40% of total global energy consumption. The International Energy Agency (IEA) and the European Commission (EC) are attempting to achieve an 80% reduction in global emissions by 2050. The objectives of this paper are to identify the refurbishment scenario with the lowest environmental impact using Life Cycle Assessment (LCA) and to assess the scenario’s robustness to future climate change scenarios using a sensitivity analysis. We applied and verified the proposed approach in a residential case study of a reference project located in Kapfernberg, Austria. The environmental assessment included two façade refurbishment proposals (minimum and high quality with respect to energy), onsite energy generation (using solar thermal collectors and photovoltaic (PV) panels), one renewable future energy mix and the effects of climate change according to the Austrian Panel on Climate Change (APCC). The environmental indicators used in the assessment were the cumulative energy demand non-renewable (CED n. ren.), global warming potential (GWP) and ecological scarcity (UBP) over building life cycles. The results indicated that a high-quality refurbishment of the thermal envelope with prefabricated façade elements, including solar thermal collectors and PV panels, represented the optimal refurbishment. In terms of the environmental indicators, the high-quality refurbishment scenario is always beneficial throughout the building’s life cycle. Additionally, the sensitivity analysis of the high-quality refurbishment scenario found an increasing production of surplus electricity with increasing PV area. This surplus of energy provides greater benefit in the short term with the current energy mix. Once the energy from the grid is shifted to renewable sources, the added benefit is decreased. Therefore, it is necessary to find an optimal balance between diminishing returns due to changes in the future energy mix and the financial investment made over the lifetime of the building, especially for plus energy buildings. However the findings from this specific case study need to be evaluated for other refurbishment cases, taking into account future local climate change and energy supply mix scenarios in other regions.