We consider the formation of molecules in primordial prestellar clumps and evaluate the line luminosities to assess detectability by next-generation observational facilities. If the initial H-2 fraction is sufficiently high, HD becomes an important coolant in the clumps. The luminosity from such HD cooling clumps is lower than that from H-2 cooling ones because of the lower temperature (< 100K). As for Li reactions, we include the three-body LiH formation approximately. The Li molecular fraction remains very low (< 10(-3)) throughout the evolution, owing to the high dissociative reaction rate of LiH + H -> Li + H-2. LiH does not become an important coolant in any density range. The luminous emission lines from the prestellar cores include H-2 rovibrational lines [1-0 Q(1), 1-0 O(3), 1-0 0(5)] and pure rotational lines [0-0 S(3), 0-0 S(4), 0-0 S(5)]. The next-generation facilities SPICA and JWST are able to detect H-2 emission in a large pre-galactic cloud that forms metal-free stars at a high rate of similar to 10(3) M-circle dot yr(-1) at a redshift of z < 10. We also derive an analytical expression for the luminosity that reproduces the numerical results.