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 0.1 arcsec brown dwarf binary GJ569Bab. We took 50 000 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 7.78 ± 0.03. The AO+LI observations at WHT were able to resolve the binary system GJ569Bab located at 4.92 ± 0.05 arcsec from GJ569A. We measure a separation of 98.4 ± 1.1 mas and I-band magnitudes of 13.86 ± 0.03 and 14.48 ± 0.03 and I-J colours of 2.72 ± 0.08 and 2.83 ± 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˜ 17 at distances larger than 1 arcsec. The I-J colours 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 per cent) more massive than Bb. We obtain new orbital parameters which are in good agreement with those in the literature. Based on service observations made with the 4.2-m William Herschel Telescope (WHT) operated on the island of La Palma by the Isaac Newton Group and on observations made with the Nordic Optical Telescope (NOT), operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.