We present the first results of the LBT Imaging of Galaxy Haloes and Tidal Structures (LIGHTS) survey. LIGHTS is an ongoing observational campaign with the 2x8.4m Large Binocular Telescope (LBT) aiming to explore the stellar haloes and the low surface brightness population of satellites down to a depth of mu_V_~31mag/arcsec^2^ (3s in 10"x10" boxes) of nearby galaxies. We simultaneously collected deep imaging in the g and r Sloan filters using the Large Binocular Cameras (LBCs). The resulting images are 60 times (i.e. 4.5mag) deeper than those from the Sloan Digital Sky Survey (SDSS), and they have characteristics comparable (in depth and spatial resolution) to the ones expected from the future Legacy Survey of Space and Time (LSST). Here we show the first results of our pilot programme targeting NGC1042 (an M33 analogue at a distance of 13.5Mpc) and its surroundings. The depth of the images allowed us to detect an asymmetric stellar halo in the outskirts of this galaxy whose mass (1.4+/-0.4x10^8^M_{sun}_) is in agreement with the Lambda Cold Dark Matter (LambdaCDM) expectations. Additionally, we show that deep imaging from the LBT reveals low mass satellites (a few times 10^5^M_{sun}_) with very faint central surface brightness mu_V(0)_~27mag/arcsec^2^(i.e. similar to Local Group dwarf spheroidals, such as Andromeda XIV or Sextans, but at distances well beyond the local volume). The depth and spatial resolution provided by the LIGHTS survey open up a unique opportunity to explore the `missing satellites' problem in a large variety of galaxies beyond our Local Group down to masses where the difference between the theory and observation (if any) should be significant.