As @srtee has explained. LAMMPS computes the angular velocity by following the inversion of L = I\omega.
The feature proposal that I posted some years ago ([Feature Proposal] Fix momentum angular for non-rigid groups of atoms) refers to implementing a computation of \omega that follows the procedure described in section II.A doi.org/10.1063/1.474493. The crux of the issue is that when you consider a group of atoms that are not a solid body (e.g. a molecule that can vibrate) then what is usually considered \omega = I^{-1}L will have some component from the vibrational motion of the constituent atoms. So in this context what is considered the “true” \omega is not exactly the same as a rigid body.
As @akohlmey has said, it’s up to you to define what \omega means in your system and you can definitely perform tests to compute \omega through different procedures (you only need positions and velocities, nothing fancy).
I have some more references on how to separate vibrational and rotational motion in molecules (again, the loose definition of molecule here just means a group of atoms that are bonded in some way, so the definition could apply to your system, I think). If that is a method that you want to pursue then I will be happy to help.