Do Li4 or Li8 molecules exist?
Yes, they do exist and were characterised spectroscopically, see here (and there is a note on similar clusters for sodium):

Blanc, J.; Bonačić‐Koutecký, V.; Broyer, M.; Chevaleyre, J.; Dugourd, P.; Koutecký, J.; Scheuch, C.; Wolf, J. P.; Wöste, L. Evolution of the electronic structure of lithium clusters between four and eight atoms. J. Chem. Phys. 1992, 96 (3), 1793–1809. DOI: 10.1063/1.462846.

They are not, however, "stable" enough to exist in solid state or even to obtain a pure gas, rather complicated arcane trickery is used to work with (very small amount of) them.

Lithium has rather complicated chemistry, easily forming polyhedral structures when bound to proper partner. For example, methyllithium is a tetramer. The simplest rationalization is that its s- and p-orbitals have very close energies and thus low-energy vacant p-orbitals participate in formation of multicentre electron-deficient bonds.