  Clustering of Lyman-$\alpha$ (Ly$\alpha$) emitting galaxies (LAEs) is a
useful probe of cosmology. However, Ly$\alpha$ radiative transfer (RT) effects,
such as absorption, line shift, and line broadening, and their dependence on
the large-scale density and velocity fields can modify the measured LAE
clustering and line intensity mapping (LIM) statistics. We explore the effect
of RT on the Ly$\alpha$ LIM power spectrum in two ways: using an analytic
description based on linear approximations and using lognormal mocks. The
qualitative effect of intergalactic Ly$\alpha$ absorption on the LIM auto- and
cross-power spectrum is a scale-dependent, reduced effective bias, reduced mean
intensity, and modified redshift-space distortions. The linear absorption model
does not describe the results of the lognormal simulations well. The random
line shift suppresses the redshift-space power spectrum similar to the
Fingers-of-God effect. In cross-correlation of LAEs or Ly$\alpha$ intensity
with a non-Ly$\alpha$ tracer, the Ly$\alpha$ line shift leads to a phase shift
of the complex power spectrum, i.e. a cosine damping of the real part. Line
broadening from RT suppresses the LIM power spectra in the same way as limited
spectral resolution. We study the impact of Ly$\alpha$ RT effects on the
Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) LAE and LIM power
spectra using lognormal mocks. We find that even small amounts of IGM
absorption will significantly change the measured LAE auto-power spectrum and
the LAE-intensity cross-power spectrum. Therefore, HETDEX will be able to
constrain Ly$\alpha$ RT effects.
