In this contribution, the structural analysis of a medieval leaning masonry tower is presented, focusing on the Garisenda Tower in Bologna (Italy), which has recently raised significant structural concerns. The study employs a geometrically accurate 3D finite element (FE) model to investigate the impact of multi-leaf material uncertainty on the tower mechanical behaviour. The structure, characterized by a 4-degree inclination, features walls with an inner infill and outer leaves of gypsum stone and clay brick masonry. The FE model is developed from a comprehensive point cloud capturing both internal and external surfaces. A novel aspect of the modelling process involves an iterative closest point (ICP) algorithm used to estimate the tower inclination. To address the lack of in-situ characterization, parametric eigenvalue analyses and nonlinear static simulations are conducted, using experimentally identified natural frequencies and mode shapes as benchmarks. The results highlight that multiple material configurations, such as combinations of soft core-stiff outer leaves or vice versa, can accurately match the empirical dynamic features, leading to significantly different internal stress distributions. Finally, the study outlines recent developments toward a Digital Twin of the tower. Within this framework, a thermo-mechanical model is currently being developed to account for environmental inputs, such as solar radiation, wind, and ambient temperature, to support the ongoing structural health monitoring and the long-term preservation of the monument.