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 Lyα, galaxy properties, and low-ionization UV lines. Galaxies with high [O iii]/[O ii] have higher Hα equivalent widths (EWs), and high intrinsic Lyα production may explain the prevalence of high Lyα EWs among GPs. While Lyα escape fraction is closely linked to low gas covering fractions, implying a clumpy gas geometry, narrow Lyα velocity peak separation (∆v Lyα ) correlates with the ionization state, suggesting a density-bounded geometry. We therefore suggest that ∆v Lyα may trace the residual transparency of low-column-density pathways. Metallicity is associated with both [O iii]/[O ii] and ∆v Lyα . 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 Lyα emission strength and is related to Lyα profile shape. However, as expected for optically thin objects, the GPs with the lowest ∆v Lyα 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.