Current market conditions characterized by technological changes, increasing regulatory requirements and low funding make current construction management models obsolete. This tendency affects not only the private housing market but also public administration projects, which have large time and budget deviations across the board. As a result, new approaches are needed to improve the efficiency of the construction process, removing extra costs and delivering projects on time. The most representative trends in the construction industry that enable such improvements are both Building Information Modelling paradigm (BIM) and Lean Construction philosophy with one of its associated tools in the field of construction management—the Last Planner System. However, a review of the literature shows the scarcity of works on the synergy of both paradigms taking into account the extensive literature on Lean and BIM individually. This is further accused if we look beyond the theoretical literature reviews. Therefore, this paper is focused on the benefits derived from the synergy of both disciplines and the impacts on project efficiency through a case study of a public construction project at the university of Alicante in order to provide empirical evidence of the benefits and improvements of using BIM at the Look Ahead meetings and of the Last Planner System. Finally, the results of the case study allow us to make a comparison with the data related to cost deviations of other public projects with different uses, built areas, and complexity which were managed with traditional methods of construction.