  We present a study on stellar properties of Lyman-alpha (Ly$\alpha$) emitters
at 5 $< z <$ 8.2. We use 247 photometrically-selected, lensed, high-redshift,
low luminosity galaxy candidates with spectroscopic follow-up. Of these, 38 are
confirmed spectroscopically to be between 5 $< z <$ 8.2 via detection of
Ly$\alpha$. For each galaxy and candidate, we estimate stellar mass, star
formation rate, specific star formation rate, and mass-weighted age with
spectral energy distribution fitting. We also measure the UV $\beta$ slope and
luminosity using values from photometry. We find no strong correlation between
Ly$\alpha$ equivalent width and any of these properties, as well as no
significant difference between the physical properties of Ly$\alpha$ emitters
and candidates without Ly$\alpha$ detected. This lack of expected trends may be
explained by a combination of the evolving opacity of the IGM at these
redshifts as well as the unique phase space probed by our lensed sample. Via
tests on other galaxy samples which show varying strengths of correlations, we
conclude that if there exist any relationships between Ly$\alpha$ EW and
physical properties in the underlying population of faint galaxies, they are
weak correlations. We also present the results of a spectroscopic search for
CIII] emission in confirmed Ly$\alpha$ emitters at $z \sim 7$, finding no CIII]
detections, but putting constraints on strong AGN activity and extreme nebular
emission.
