  Combining 66 ultraviolet (UV) spectra and ancillary data from the
Low-Redshift Lyman Continuum Survey (LzLCS) and 23 LyC observations by earlier
studies, we form a statistical sample of star-forming galaxies at $z \sim 0.3$
to study the role of the cold interstellar medium (ISM) gas in the leakage of
ionizing radiation. We first constrain the massive star content (ages and
metallicities) and UV attenuation, by fitting the stellar continuum with a
combination of simple stellar population models. The models, together with
accurate LyC flux measurements, allow to determine the absolute LyC photon
escape fraction for each galaxy ($f_{\rm esc}^{\rm abs}$). We measure the
equivalent widths and residual fluxes of multiple HI and low-ionization state
(LIS) lines, and the geometrical covering fraction adopting the picket-fence
model. The $f_{\rm esc}^{\rm abs}$ spans a wide range, with a median (0.16,
0.84 quantiles) of 0.04 (0.02, 0.20), and 50 out of the 89 galaxies detected in
the LyC. The HI and LIS line equivalent widths scale with the UV luminosity and
attenuation, and inversely with the residual flux of the lines. The HI and LIS
residual fluxes are correlated, indicating that the neutral gas is spatially
traced by the LIS transitions. We find the observed trends of the absorption
lines and the UV attenuation are primarily driven by the covering fraction. The
non-uniform gas coverage demonstrates that LyC photons escape through
low-column density channels in the ISM. The equivalent widths and residual
fluxes of the UV lines strongly correlate with $f_{\rm esc}^{\rm abs}$: strong
LyC leakers show weak absorption lines, low UV attenuation, and large
Ly$\alpha$ equivalent widths. We finally show that simultaneous UV absorption
line and dust attenuation measurements can predict, on average, the escape
fraction of galaxies and the method can be applied to galaxies across a wide
redshift range.
