High-resolution X-ray spectroscopy and polarimetry provided by XRISM and IXPE offer new
diagnostics of the geometry and kinematics of photo-ionised plasmas around compact
objects. Interpreting reprocessed X-ray emission in such systems requires full
three-dimensional radiative transfer (3D RT) including photon-ion interactions.

We extend the Monte Carlo (MC) RT code SKIRT by implementing the Lyman-series lines of
H-like ions, enabling selfconsistent modelling of resonant scattering, radiative
recombination, and polarisation of these lines in X-ray photo-ionised plasmas.

We implemented Lyman-series transitions (up to n = 10) for ions with Z = 2-30,
including fine-structure splitting and linear polarisation in resonant scattering. Two
channels for the production of the Lyman-series lines (resonant scattering and radiative
recombination) are considered. The microphysics (cross-sections, branching ratios, and
redistribution functions) are validated against analytical solutions and compared with
the 1D RT code Cloudy based on the two-stream solver. We further demonstrate the
capabilities of the code using idealised setups and a 3D AGN geometry.

The implementation reproduces analytical expectations and shows good agreement with
Cloudy. The SKIRT simulations naturally capture RT effects such as P Cygni profiles and
line-profile distortion in optically thick media, which are inaccessible to the
conventional 1D RT codes commonly used in X-rays. In 3D geometries, we find that
anisotropic illumination and velocity fields significantly modify the Lyman series line
ratios and profiles, all of which are observable with XRISM.

The extended version of SKIRT provides a powerful framework for interpreting X-ray line
spectra and polarisation from photo-ionised plasmas. It is particularly suited for
constraining the geometry and velocity structure in the vicinity of compact objects in
the XRISM and IXPE era.