  We present a detailed characterization of the Lya properties for 93 Lya
emitters (LAEs) at z~3.1 selected from the D1 field of the
Canada-France-Hawaii-Telescope Legacy Survey, including 24 members of a massive
protocluster. The median-stacked Lya image shows an extended Lya halo (LAH)
surrounding the galaxy with the exponential scale length 4.9+/-0.7kpc, which
accounts for roughly half of the total line flux. Accounting for the LAH
contribution, the total Lya escape fraction, f_esc, is 40+/-26%. Combining the
dataset with existing measurements, we find a dependence of f_esc on the
galaxy's UV slope (beta) and UV luminosity (L_UV). The simultaneous use of both
parameters allows prediction of f_esc within 0.18dex, a substantial improvement
over 0.23dex when only beta is used. The correlation between f_esc and E(B-V)
suggests that Lya photons undergo interstellar dust attenuation in a similar
manner to continuum photons. Yet, Lya transmission is typically higher than
that expected for continuum photons at similar wavelength by a factor, which
depends on UV luminosity, up to 2 in the samples we studied. These results hint
at complex geometries and physical conditions of the interstellar medium, which
affect the Lya transmission or production. Alternatively, the dust law may
change with luminosity leading to over-or under-estimation of f_esc. Finally,
we report that protocluster member LAEs tend to be bluer and more UV-luminous
than their field cousins, resulting in systematically higher f_esc values. We
speculate that it may be due to the widespread formation of young low-mass
galaxies in dense gas-rich environments.
