The debate on the relevance of the global sustainability (including energy, environmental, social, economic, and political aspects) of building stock is becoming increasingly important in Europe. In this context, special attention is placed on the refurbishment of existing buildings, in particular those characterized by significant volumes and poor energy performance. Directive 2012/27/EU introduced stringent constraints (often disregarded) for public administrations to ensure a minimum yearly renovation quota of its building stock. This study describes how Life Cycle Cost analysis (LCC) can be used as a tool to identify the “cost-optimal level” among different design solutions to improve the energy performance of existing buildings. With this aim, a social housing building located in the town of Pisa (Italy) was chosen as the case study, for which two alternative renovation designs were compared using the LCC methodology to identify the optimal solution. The two alternatives were characterized by the same energy performance—one was based on the demolition of the existing building and the construction of a new building (with a wooden frame structure, as proposed by the public company owner of the building), while the other was based on the renovation of the existing building. This study can provide useful information, especially for designers and public authorities, about the relevance of the economic issues related to the renovation of social housing in a Mediterranean climate.