The potential of combining Adaptive Optics (AO) and Lucky Imaging (LI) to achieve high precision astrometry and differential photometry in the optical is investigated by conducting observations of the close 0farcs1 brown dwarf binary GJ569Bab. We took 50000 $I$-band images with our LI instrument FastCam attached to NAOMI, the 4.2-m William Herschel Telescope (WHT) AO facility. In order to extract the most of the astrometry and photometry of the GJ569Bab system we have resorted to a PSF fitting technique using the primary star GJ569A as a suitable PSF reference which exhibits an $I$-band magnitude of $7.78pm0.03$. The AO+LI observations at WHT were able to resolve the binary system GJ569Bab located at $4farcs 92 pm 0farcs05$ from GJ569A. We measure a separation of $98.4 pm 1.1$ mas and $I$-band magnitudes of $13.86 pm 0.03$ and $14.48 pm 0.03$ and $I-J$ colors of 2.72$pm$0.08 and 2.83$pm$0.08 for the Ba and Bb components, respectively. Our study rules out the presence of any other companion to GJ569A down to magnitude I$sim$ 17 at distances larger than 1arcsec. The $I-J$ colors measured are consistent with M8.5-M9 spectral types for the Ba and Bb components. The available dynamical, photometric and spectroscopic data are consistent with a binary system with Ba being slightly (10-20%) more massive than Bb. We obtain new orbital parameters which are in good agreement with those in the literature.
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