We introduce turboMagnon, an implementation of the Liouville-Lanczos approach to linearized time-dependent density-functional theory, designed to simulate spin-wave spectra in solid-state materials. The code is based on the noncollinear spin-polarized framework and the self-consistent inclusion of spin-orbit coupling that allow to model complex magnetic excitations. The spin susceptibility matrix is computed using the Lanczos recursion algorithm that is implemented in two flavors -the non-Hermitian and the pseudo-Hermitian one. turboMagnon is open-source software distributed under the terms of the GPL as a component of QUANTUM ESPRESSO. As with other components, turboMagnon is optimized to run on massively parallel architectures using native mathematical libraries (LAPACK and FFTW) and a hierarchy of custom parallelization layers built on top of MPI. The effectiveness of the code is showcased by computing magnon dispersions for the CrI3 monolayer, and the importance of the spin-orbit coupling is discussed. (C) 2022 The Author(s). Published by Elsevier B.V.