  We present results from WIYN pODI imaging of Lacerta I (And XXXI), a
satellite dwarf galaxy discovered in the outskirts of the Andromeda galaxy
(M31) in Pan-STARRS1 survey data. Our deep, wide-field $g,i$ photometry reaches
$\sim$3 magnitudes fainter than the photometry in the Pan-STARRS1 discovery
paper and allows us to trace the stellar population of Lac I beyond two
half-light radii from the galaxy center. We measure a Tip of the Red Giant
Branch (TRGB) distance for Lac I of $(m-M)_0=24.44\pm0.11$ mag (773$\pm$40 kpc,
or 264$\pm$6 kpc from M31), which is consistent with the Pan-STARRS1 distance.
We use a maximum-likelihood technique to derive structural properties for the
galaxy, and find a half-light radius ($r_h$) of 3.24$\pm$0.21 arcmin
(728$\pm$47 pc), ellipticity ($\epsilon$) of 0.44$\pm$0.03, total magnitude
$M_V$ $=$ $-$11.4$\pm$0.3, and central surface brightness $\mu_{V,0}$ $=$
24.8$\pm$0.3 mag arcsec$^{-2}$. We find no HI emission in archival data and set
a limit on Lac I's neutral gas mass-to-light ratio of $M_{HI}/L_V$ $<$ 0.06
$M_{sun}$/$L_{sun}$, confirming Lac I as a gas-poor dwarf spheroidal galaxy.
Photometric metallicities derived from Red Giant Branch stars within 2 $r_h$
yield a median [Fe/H] of $-$1.68$\pm$0.03, which is more metal-rich than the
spectroscopically-derived value from Martin et al. (2014). Combining our
measured magnitude with this higher metallicity estimate places Lac I closer to
its expected position on the luminosity-metallicity relation for dwarf
galaxies.
