  Long gamma-ray bursts (GRBs) have been suggested to occur preferentially in
low metallicity environment. We discuss the possibility and theoretical aspects
of using Lyman alpha emission properties of long GRB host galaxies as a
metallicity indicator of high redshift GRB environments, where direct
metallicity measurements are not easy. We propose to use the fraction of
Ly-alpha emitters (LAEs) in long GRB host galaxies as a function of UV
luminosity, which can be compared with star-formation-rate weighted LAE
fraction of Lyman-break galaxies as the standard in the case of no metallicity
dependence. There are two important effects of metallicity dependence of long
GRB rate to change the LAE fraction of host galaxies. One is the enhancement of
intrinsic Ly-alpha equivalent width (EW) by stronger ionizing UV luminosity of
low metallicity stellar population, and the other is extinction by interstellar
dust to change the observable EW. Based on a latest theoretical model of LAEs
that reproduce observations, we argue that the latter is likely to work in the
opposite direction to the former, i.e., to decrease LAE fraction if GRBs
preferentially occur in low-metallicity environments, because of the clumpy
inter-stellar medium effect. The high LAE fraction of GRB host galaxies
indicated by observations is quantitatively be explained by the LAE model if
GRBs occur when Z < 0.1Z_sun, although this result is still indicative because
of the limited statistics and theoretical uncertainties. This result
demonstrates that the LAE statistics of GRB hosts may give us useful
information in the future.
