  Lyman break analogs in the local Universe serve as counterparts to Lyman
break galaxies (LBGs) at high redshifts, which are widely regarded as major
contributors to cosmic reionization in the early stages of the Universe. We
studied XMM-Newton and Chandra observations of the nearby LBG analog Haro 11,
which contains two X-ray-bright sources, X1 and X2. Both sources exhibit Lyman
continuum (LyC) leakage, particularly X2. We analyzed the X-ray variability
using principal component analysis (PCA) and performed spectral modeling of the
X1 and X2 observations made with the Chandra ACIS-S instrument. The PCA
component, which contributes to the X-ray variability, is apparently associated
with variable emission features, likely from ionized superwinds. Our spectral
analysis of the Chandra data indicates that the fainter X-ray source, X2 (X-ray
luminosity $L_{\rm X} \sim 4 \times 10^{40} $ erg s$^{-1}$), the one with
higher LyC leakage, has a much lower absorbing column ($N_{\rm H} \sim 1.2
\times 10^{21}$ cm$^{-2}$) than the heavily absorbed luminous source X1
($L_{\rm X} \sim 9 \times 10^{40} $ erg s$^{-1}$ and $N_{\rm H} \sim 11.5
\times 10^{21}$ cm$^{-2}$). We conclude that X2 is likely less covered by
absorbing material, which may be a result of powerful superwinds clearing
galactic channels and facilitating the escape of LyC radiation. Much deeper
X-ray observations are required to validate the presence of potential
superwinds and determine their implications for the LyC escape.
