  As some of the only Lyman continuum (LyC) emitters at z~0, Green Pea (GP)
galaxies are possible analogs of the sources that reionized the universe. We
present HST COS spectra of 13 of the most highly ionized GPs, with [O III]/[O
II]=6-35, and investigate correlations between Ly-alpha, galaxy properties, and
low-ionization UV lines. Galaxies with high [O III]/[O II] have higher H-alpha
equivalent widths (EWs), and high intrinsic Ly-alpha production may explain the
prevalence of high Ly-alpha EWs among GPs. While Ly-alpha escape fraction is
closely linked to low gas covering fractions, implying a clumpy gas geometry,
narrow Ly-alpha velocity peak separation (delta_v,LyA) correlates with the
ionization state, suggesting a density-bounded geometry. We therefore suggest
that delta_v,LyA may trace the residual transparency of low-column-density
pathways. Metallicity is associated with both [O III]/[O II] and delta_v,LyA.
This trend may result from catastrophic cooling around low-metallicity star
clusters, which generates a compact geometry of dense clouds within a
low-density inter-clump medium. We find that the relative strength of
low-ionization UV emission to absorption correlates with Ly-alpha emission
strength and is related to Ly-alpha profile shape. However, as expected for
optically thin objects, the GPs with the lowest delta_v,LyA show both weak
low-ionization emission and weak absorption. The strengths of the
low-ionization absorption and emission lines in a stacked spectrum do not
correspond to any individual spectrum. Galaxies with high [O III]/[O II]
contain a high fraction of LyC emitter candidates, but [O III]/[O II] alone is
an insufficient diagnostic of LyC escape.
