  The first galaxies in the Universe are built up where cold dark matter (CDM)
forms large scale filamentary structure. Although the galaxies are expected to
emit numerous Lya photons, they are surrounded by plentiful neutral hydrogen
with a typical optical depth for Lya of ~10^5 (HI halos) before the era of
cosmological reionization. The HI halo almost follows the cosmological Hubble
expansion with some anisotropic corrections around the galaxy because of the
gravitational attraction by the underlying CDM filament. In this paper, we
investigate the detectability of the Lya emissions from the first galaxies,
examining their dependence on viewing angles. Solving the Lya line transfer
problem in an anisotropically expanding HI halo, we show that the escape
probability from the HI halo is the largest in direction along the filament
axis. If the Lya source is observed with a narrow-band filter, the difference
of apparent Lya line luminosities among viewing angles can be a factor of > 40
at an extreme case. Furthermore, we evaluate the predicted physical features of
the Lya sources and flux magnification by gravitational lensing effect due to
clusters of galaxies along the filament. We conclude that, by using the next
generation space telescopes like the JWST, the Lya emissions from the first
galaxies whose CDM filament axes almost face to us can be detected with the S/N
of > 10.
