A novel technique for high-resolution 1.5 µm photonics-enabled terahertz (THz) spectroscopy using software control of the illumination spectral line shape (SLS) is presented. The technique enhances the performance of a continuous-wave THz spectrometer to reveal previously inaccessible details of closely spaced spectral peaks. We demonstrate the technique by performing spectroscopy on LiYF₄:Ho³⁺, a material of interest for quantum science and technology, where we discriminate between inhomogeneous Gaussian and homogeneous Lorentzian contributions to absorption lines near 0.2 THz. Ultra-high-resolution (<100 Hz full-width at half maximum) frequency-domain spectroscopy with quality factor Q > 2 × 10⁹ is achieved using an exact frequency spacing comb source in the optical communications band, with a custom uni-traveling-carrier photodiode mixer and coherent down-conversion detection. Software-defined time-domain modulation of one of the comb lines is demonstrated and used to resolve the sample SLS and to obtain a magnetic field-free readout of the electronuclear spectrum for the Ho³⁺ ions in LiYF₄:Ho³⁺. In particular, homogeneous and inhomogeneous contributions to the spectrum are readily separated. The experiment reveals previously unmeasured information regarding the hyperfine structure of the first excited state in the ⁵I₈ manifold complementing the results reported in Phys. Rev. B 94, 205132 (2016).