Good question, you may recall that there exists diagonal relationships in early members of different groups in the periodic table leading to unusual behaviour for that group. Li and Mg share a diagonal relationship because in Li->Na there is a decrease in charge density, but from Na->Mg there is an increase. It is known that Li and Mg share similar chemistry due to the similarity in the degree of covalency in their compounds.
Lithium has a comparatively low conductivity because of its high ionization energy relative to the others; that is, it "cheats" (on average, delocalizes less than 1 mole of electrons per mole of atoms), so its conductivity is lower than expected. The same rationale can be applied to the Group 2 elements which are divalent, where the conductivity of magnesium (and Be) is low in comparison to the others. This suggests that this higher ionization energies limit delocalization to fewer than 2 moles of electrons per mole of atoms. This could explain the comparatively low melting point of Mg. If fewer than two electrons are delocalized, then the resulting lattice energy must be lowered accordingly.