We present the first results of our pilot study of eight photometrically selected Lyman-continuum (LyC) emitting galaxy candidates from the COSMOS field and focus on their optical emission line ratios. Observations were performed in the H and K bands using the Multi-Object Spectrometer for Infra-Red Exploration (MOSFIRE) instrument at the Keck Observatory, targeting the [O II], H β, and [O III] emission lines. We find that photometrically selected LyC emitting galaxy candidates have high ionization parameters, based on their high [O III]/[O II] ratios (O32), with an average ratio for our sample of 2.5 ± 0.2. Preliminary results of our companion Low-Resolution Imaging Spectrometer (LRIS) observations, targeting LyC and Ly α, show that those galaxies with the largest O32 are typically found to also be Ly α emitters. High O32 galaxies are also found to have tentative non-zero LyC escape fractions (f_esc(LyC)) based on u band photometric detections. These results are consistent with samples of highly ionized galaxies, including confirmed LyC emitting galaxies from the literature. We also perform a detailed comparison between the observed emission line ratios and simulated line ratios from density bounded H II regions modelled using the photoionization code MAPPINGS V. Estimates of f_esc(LyC) for our sample fall in the range from 0.0 to 0.23 and suggest possible tension with published correlations between O32 and f_esc(LyC), adding weight to dichotomy of arguments in the literature. We highlight the possible effects of clumpy geometry and mergers that may account for such tension.