We have re-analyzed FUSE data and obtained new Chandra observations of Haro 11, a local (D_L=88 Mpc) UV luminous galaxy. Haro 11 has a similar far-UV luminosity (10^10.3 L_odot), UV surface brightness (10^9.4 L_odot kpc^-2), SFR, and metallicity to that observed in Lyman Break Galaxies (LBGs). We show that Haro 11 has extended, soft thermal (kT~0.68 keV) X-ray emission with a luminosity and size which scales with the physical properties (e.g. SFR, stellar mass) of the host galaxy. An enhanced alpha/Fe, ratio of ~4 relative to solar abundance suggests significant supernovae enrichment. These results are consistent with the X-ray emission being produced in a shock between a supernovae driven outflow and the ambient material. The FUV spectra show strong absorption lines similar to those observed in LBG spectra. A blueshifted absorption component is identified as a wind outflowing at ~200-280 km/s. OVIlambdalambda1032,1038 emission, the dominant cooling mechanism for coronal gas at T~10^5.5 K is also observed. If associated with the outflow, the luminosity of the OVI emission suggests that <20% of the total mechanical energy from the supernovae and solar winds is being radiated away. This implies that radiative cooling through OVI is not significantly inhibiting the growth of the outflowing gas. In contradiction to the findings of Bergvall et al 2006, we find no convincing evidence of Lyman continuum leakage in Haro 11. We conclude that the wind has not created a `tunnel allowing the escape of a significant fraction of Lyman continuum photons and place a limit on the escape fraction of f_{esc}<2%. Overall, both Haro 11 and a previously observed LBG analogue VV 114, provide an invaluable insight into the X-ray and FUV properties of high redshift LBGs.