Vortex crystals are geometric arrays of vortices found in various physics fields, owing their regular internal structure to mutual interactions within a spatially confined system. In optics, vortex crystals may form spontaneously within a nonlinear resonator but their usefulness is limited by the lack of control over their topology. On the other hand, programmable devices used in free space, like spatial light modulators, allow the design of nearly arbitrary vortex distributions but without any intrinsic dynamics. By combining non-Hermitian optics with on-demand topological transformations enabled by metasurfaces, we report a solid-state laser that generates vortex crystals with mutual interactions and actively-tunable topologies. We demonstrate 10x10 coherent vortex arrays with nonlocal coupling networks that are not limited to nearest-neighbor coupling but rather dictated by the crystal's topology. The vortex crystals exhibit sharp Bragg diffraction peaks, witnessing their coherence and high topological charge purity, which we resolve spatially over the whole lattice by introducing a parallelized analysis technique. By structuring light at the source, we enable complex transformations that allow to arbitrarily partition the orbital angular momentum inside the cavity and to heal topological charge defects, making these resonators a robust and versatile tool for advanced applications in topological optics.