An extensive experimental campaign has been started within the frame of the project REVHEAL (Structural Rehabilitation of Vaults in Heritage Asset Learning), funded by the Italian PRIN 2022 PNRR research program, to investigate the behavior of masonry cross vaults subjected to in-plane shear resulting from lateral displacements at the abutments due to seismic actions. To replicate the seismic action occurring in real case, a full-scale cross vault has been constructed in the laboratory of structural engineering of the University of Brescia, where a test rig has been arranged to replicate the effects of the seismic action by means of a quasi-static reverse cyclic lateral displacement applied at two moving abutments of the vault specimen. Unlike the few similar tests reported in the literature, the one presented here features a geometrical configuration typical of heritage constructions, with arches along three of the four vault edges and a perimeter wall leant on the remaining edge. The test aims at investigating the behavior of the structure before and after retrofitting with a Fiber Reinforced Cementitious Mortar (FRCM) based technique, which involves the application of a basalt fiber mesh properly connected only to the vault’s extrados. Synergy between Geomatics and Structural Engineering has been pursued to build reality-based models suitable to consider some aspects that are usually neglected in the analysis of historical masonry constructions, such as the as-built deformed geometry and the block arrangement. The present paper refers to the first phase of the research program, which includes the first loading cycles performed to simulate severe pre-damaging typical of a structure approaching its ultimate capacity. Therefore, in addition to the outcomes of material characterization tests, the manuscript reports and discusses the results of the cyclic test, with a focus on the specimen’s strength, damage evolution, and displacement capacity. An integrated 3D metric survey campaign was developed, aimed at obtaining dense point clouds with RGB information by means of LiDAR acquisitions and close-range photogrammetry. Moreover, multiple sets of topographic survey measurements were conducted for supporting quality of models and ensuring high-accuracy information. The experimental findings, based also on deviation maps computed from the multiple test-time-related 3D digital models, are compared with the results of preliminary simulations carried out using three-dimensional nonlinear Finite Element models, the latter also used to predict the vault’s response after strengthening with a FRCM overlay. The simulation results provide valuable insights for properly designing the details of the FRCM-based technique adopted to repair the full-scale specimen, which will be tested in the second phase of the research program.