Because iodine itself is only moderately non-metallic, and lithium is not one of the most metallic (roughly comparable to or slightly stronger than Mg), resulting in the difference in electronegativity between the two actually not being very large, Li being about 0.9 and I about 2.4, a difference of 1.5, which falls within the range of polar ****-valence bonds (1.7 is generally used as the cutoff point between polar ****-valence and ionic bonding, because at this point the compound is ionic is about 50%, but this is not the only basis) and is therefore a ****valence bond. (Similar to the ****valence of AlCl3)
In addition to this, interpreting this in terms of ionic polarization, LiI would be given significant ****valence due to the fact that both Li+ and I- are relatively polarizable, resulting in a lower melting and boiling point than common ionic crystals.
Other common metal-nonmetal compounds that are ****-valent in high school include AgCl, AgBr, AgI, FeBr3, BeCl2 (which is slightly more ionic), and so on.