Understanding the mechanisms driving the escape of ionizing or Lyman continuum (LyC) emission from the interstellar medium of galaxies is necessary to constrain the evolution of reionization and the sources responsible for it. While progress has been made in identifying the global galaxy properties linked to the ionizing escape fraction , little is currently known about how spatially resolved galaxy properties impact it. We present Hubble Space Telescope (HST) imaging data obtained in the Lyα and Continuum Origins Survey (LaCOS). LaCOS consists of HST imaging covering rest-frame optical and UV bands for a subsample of 42 galaxies in the Low redshift Lyman Continuum Survey, including 22 LyC emitters (). Here, we describe the sample, observations, and data reduction, and investigate connections between global and sub-kiloparsec Lyα emission and . We confirm the correlation between and EWLyα, and the anticorrelation with r50, when using values obtained via global photometry. We also find correlations previously found with spectroscopy with global photometric LLyα, , ΣSFR, and , but with a smaller degree of correlations (). We find correlations are strongest between Lyα observables (LLyα, EWLyα) and when measured in a small aperture around the brightest UV source in each galaxy. We interpret these results as evidence that LyC photons escaping on the line of sight are contributed by a small number of UV-bright compact regions in most galaxies in LaCOS.