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In the absence of structural asymmetry, the lunar tidal Love numbers should be order independent. Through careful analysis of GRAIL’s non-static gravity field, a recent study by Park et al. (2025; Nature) extracted statistically different ordered Love numbers for the monthly Moon tides, indicative of large scale laterally varying internal structure. In their study, they inverted for variations in shear modulus within the lunar mantle and interpreted these variations in the context of temperature variations. In a complementary, though distinct vein, we jointly invert these new Love numbers, augmented with the same Love numbers for the yearly tides, in tandem with the free-air gravity field and the center-of-mass to center-of-figure offset, to produce a long-wavelength tomographic model of the Moon’s mantle density, elastic, and anelastic properties. To do this, we adapted a normal mode perturbation theory able to predict tidal deformation derived for the Earth that incorporates the Moon's rotation, lateral variations in density, shear and bulk moduli, attenuation, and boundary topography such as the crustal-mantle interface and the core-mantle boundary (Lau et al., 2015; GJI). Since we self-consistently solve for density, shear modulus and attenuation, we are able to interpret our results in the context of both temperature and compositional variations, finding a lower contribution to variations in temperature than in Park et al.’s work and independent density variations within the nearside-farside mantle asymmetry.