Context. Nearby clusters of galaxies, z ≲ 0.1, are cosmic structures still under formation. Understanding the thermodynamic properties of merging clusters can provide crucial information on how they grow in the local universe. Aims. A detailed study of the intra-cluster medium (ICM) properties of un-relaxed systems is essential to understand the fate of in-falling structures and, more generally, the virialization process. Methods. We analyzed a mosaic of XMM-Newton observations (240 ks) of the Lyra system (z ∼ 0.067) that shows a complex dynamical state. Results. We find the main cluster RXC J1825.3+3026 to be in a late merger phase, whereas its companion CIZA J1824.1+3029 is a relaxed cool-core cluster. We estimate a mass ratio of ∼1 : 2 for the pair. No diffuse X-ray emission is found in the region between them, indicating that these clusters are in a pre-merger phase. We found evidence of a galaxy group infalling on RXC J1825.3+3026 in an advanced state of disruption. The SG, one of the brightest galaxies in the Lyra complex, was very likely at the center of the infalling group. This galaxy has a gaseous “corona” indicating that it was able to retain some of its gas after the ram-pressure stripping of the intra-group medium. In this scenario the diffuse emission excess observed southwest of RXC J1825.3+3026 could be due to gas once belonging to the group and/or to cluster ICM dislocated by the passage of the group. Finally, we identified three high-velocity galaxies aligned between RXC J1825.3+3026 and the SG, two of these showing evidence of gas stripped from them during infall. We estimate them to be currently falling onto the main cluster at an infall velocity of ∼3000 km s⁻¹. Conclusions. Our study of the Lyra complex provides important clues about the processes presiding over the virialization of massive clusters in the local Universe.