Research on irregular stone masonry walls is hampered by the lack of detailed geometrical models of their internal micro-structure, i.e. the shape and size of each stone and its position within the wall. Without such a geometric digital twin of walls tested in the laboratory, it is difficult to evaluate the accuracy of existing numerical simulation techniques. Here, we describe the generation of geometrical digital twins of three irregular stone masonry walls built in the laboratory. We labelled each stone manually and then obtained the geometry of the individual stones using a portable laser scanning device. With the same device we scanned the wall after the construction of each layer. We then registered the position of each stone in the layer. This paper outlines the methodology for the data acquisition and digital reconstruction and presents the datasets for the walls. The developed geometrical digital twins provide unique information regarding the micro-structure of constructed walls that is key for the development and validation of numerical simulation techniques for stone masonry.