Low productivity in the construction industry is a long-standing issue. Over the years, stakeholders have developed strategies to address it, resulting in the emergence of two types of approaches. The first is “managerial,” where the lean construction (LC) philosophy, with its principles and tools, is recognized as one of its most important contributors. LC focuses on increasing value for the client, reducing waste and improving the performance of management practices at each stage of the construction projects. The second approach is “technological,” aiming to facilitate the connection between the cyber and physical worlds. Within this second approach, the digital twin (DT) concept is highlighted as one of the most promising technologies bridging both the cyber and physical worlds. To contribute to the body of knowledge on construction progress monitoring, this article first argues the necessity of a synergistic connection between both LC and DT. Secondly, it proposes a maturity model (MM) to conceptualize such an integration. This study is structured as follows: In the first part, a brief introduction exposes the general considerations. The second part summarizes the literature review concerning the integration in the construction phase of some concepts and tools belonging to the managerial and technological approaches, and its associated challenges. In the third part, an analysis of the theoretical feasibility of the proposed synergy is developed, based on a synthesis of the literature review. In the fourth part, a maturity model describing the types of synergic functionalities between both LC and DT for construction progress monitoring purposes is presented and explained. Finally, in the last part, a discussion about the proposed synergy, along with future trends in this domain are presented.