Identifying the mechanisms driving the escape of Lyman Continuum (LyC) photons is crucial to find Lyman Continuum Emitter (LCE) candidates. To understand the physical properties involved in the leakage of LyC photons, we investigate the connection between the HI covering fraction, HI velocity width, the Lyman alpha (LyA) properties and escape of LyC photons in a sample of 22 star-forming galaxies including 13 LCEs. We fit the stellar continua, dust attenuation, and absorption lines between 920 and 1300 A to extract the HI covering fractions and dust attenuation. Additionally, we measure the HI velocity widths of the optically thick Lyman series and derive the LyA equivalent widths (EW), escape fractions (fesc), peak velocities and fluxes at the minimum of the LyA profiles. Overall, we highlight strong correlations between the presence of low HI covering fractions and (1) low LyA peak velocities; (2) more flux at the profile minimum; and (3) larger EW(LyA), fesc(LyA), and fesc(LyC). Hence, low column density channels are crucial ISM ingredients for the leakage of LyC and LyA photons. Additionally, galaxies with narrower HI absorption velocity widths have higher LyA equivalent widths, larger LyA escape fractions, and lower LyA peak velocity separations. This suggests that these galaxies have low HI column density. Finally, we find that dust regulates the amount of LyA and LyC radiation that actually escapes the ISM. Overall, the ISM porosity is one origin of strong LyA emission and enables the escape of ionizing photons in low-z leakers. However, this is not enough to explain the largest fesc(LyC) observed, which indicates that the most extreme LCEs are likely density-bounded along all lines of sight to the observer. Overall, the neutral gas porosity constrains a lower limit to the escape fraction of LyC and LyA photons, providing a key estimator of the leakage of ionizing photons.