Two new lithium–magnesium phosphates LiMg₆(PO₄)₃(P₂O₇) and Li(Mg_5.62Sc_0.19Li_0.19)(PO₄)₃(P₂O₇) were synthesized by a solid-phase method. Using high-resolution time-of-flight neutron powder diffraction (TOF NPD) and X-ray powder diffraction (XRPD), we established that these phosphates have a Pnma orthorhombic structure with the cell parameters a = 9.14664(5) Å, b = 18.83773(8) Å, c = 8.27450(4) Å, and V = 1425.71(1) ų and a = 9.14516(5) Å, b = 18.84222(9) Å, c = 8.28204(4) Å, and V = 1427.12(1) ų, respectively. The crystal structures can be described by stacking of the [Mg₆O₁₈]_∞ or [Mg_5.62Sc_0.19Li_0.19O₁₈]_∞ wavy layers, which are parallel to the (100) direction and interconnected through PO₄ tetrahedra and P₂O₇ groups to form a 3D-framework. The Li atoms are located in large tunnels formed in a 3D lattice, which contributes to lithium diffusion. AC impedance spectroscopy analysis shows that LiMg₆(PO₄)₃(P₂O₇) and Li(Mg_5.62Sc_0.19Li_0.19)(PO₄)₃(P₂O₇) have a Li ion conductivity of 3.6 × 10⁻⁴ S cm⁻¹ and 1.7 × 10⁻⁴ S cm⁻¹ at 950 °C, with an activation energy of 1.28 eV and 1.55 eV, respectively. NMR MAS studies confirmed the coexistence of pyro- and orthogroups in the structure of both phases and two lithium positions in Li(Mg_5.62Sc_0.19Li_0.19)(PO₄)₃(P₂O₇). The first-principles method was used to study the electronic structure and stability of the two phases. The calculated formation enthalpies demonstrated that Sc is a stabilizing impurity in LiMg₆(PO₄)₃(P₂O₇), while a strong destabilization of olivine LiMgPO₄ is observed upon doping with Sc. This explains the failure to synthesize Sc-doped olivine. The new phosphate LiMg₆(PO₄)₃(P₂O₇) is a dielectric with a band gap of 5.35 eV, which decreases to 4.85 eV due to the appearance of a localized Sc 3d peak upon doping with Sc. These findings are consistent with the results obtained by UV-Vis spectroscopy. The new phase may be a good optical matrix similar to LiMgPO₄.