  We present the results of a photometric and spectroscopic survey of 321 Lyman
break galaxies (LBGs) at z ~ 3 to investigate systematically the relationship
between Lya emission and stellar populations. Lya equivalent widths (EW) were
calculated from rest-frame UV spectroscopy and optical/near-infrared/Spitzer
photometry was used in population synthesis modeling to derive the key
properties of age, dust extinction, star formation rate (SFR), and stellar
mass. We directly compare the stellar populations of LBGs with and without
strong Lya emission, where we designate the former group (EW > 20 AA) as Lya
emitters (LAEs) and the latter group (EW < 20 AA) as non-LAEs. This controlled
method of comparing objects from the same UV luminosity distribution represents
an improvement over previous studies in which the stellar populations of LBGs
and narrowband-selected LAEs were contrasted, where the latter were often
intrinsically fainter in broadband filters by an order of magnitude simply due
to different selection criteria. Using a variety of statistical tests, we find
that Lya equivalent width and age, SFR, and dust extinction, respectively, are
significantly correlated in the sense that objects with strong Lya emission
also tend to be older, lower in star formation rate, and less dusty than
objects with weak Lya emission, or the line in absorption. We accordingly
conclude that, within the LBG sample, objects with strong Lya emission
represent a later stage of galaxy evolution in which supernovae-induced
outflows have reduced the dust covering fraction. We also examined the
hypothesis that the attenuation of Lya photons is lower than that of the
continuum, as proposed by some, but found no evidence to support this picture.
