We report on the electrodynamic properties of the single crystalline lead-substituted M-type barium hexaferrite, Ba 0.3 Pb 0.7 Fe 12 O 19 , performed in the broad frequency range including radio-frequency, terahertz and sub-terahertz bands, which are particularly important for the development of microelectronic devices. We demonstrate how changing on a molecular level the chemical characteristics (composition, intermolecular interaction, spin-orbital interaction) of lead-substituted M-type hexaferrite influences its radio-frequency and terahertz electrodynamic response. Our results indicate a critical temperature range, 50 K<T<70 K, where significant changes of the electrodynamic response occur that are interpreted as freezing of dynamical oscillations of bi-pyramidal Fe(2b) ions. In the range 5-300 K, the heat capacity shows no sign of any phase transition and is solely determined by electron and phonon contributions. An anomalous electrodynamic response is detected at 1-2 THz that features a rich set of absorption resonances which are associated with electronic transitions within the fine-structured Fe 2+ ground state and are visualized in the spectra due to magnetostriction and electron-phonon interaction. We show that lead substitution of barium in barium hexaferrite, BaFe 12 O 19 , leads to the emergence of a pronounced dielectric and magnetic relaxational dynamics at radio-frequencies and that both dynamics have the same characteristic relaxation times, thus evidencing the bi-relaxor-like nature of Ba 0.3 Pb 0.7 Fe 12 O 19 . We associate the origin of the relaxations as connected with the motion of magnetic domain walls. In order to unveil crucial influence of chemical substitution on electrodynamic characteristics of the compound, we analyze our results on substituted compound in comparison with the data available for pristine barium (BaFe 12 O 19 ) and pristine lead (PbFe 12 O 19 ) hexaferrites. The obtained spectroscopic data on the dielectric properties of Ba 0.3 Pb 0.7 Fe 12 O 19 provide insight into fundamental phenomena responsible for the absorption mechanisms of the compound and demonstrates that chemical ionic substitution is an effective tool to tune the dielectric properties of the whole family of hexaferrites.