Looking into the faintEst WIth MUSE (LEWIS) is an ESO large observing programme that aims at obtaining the first homogeneous integral-field spectroscopic survey of 30 extremely low-surface-brightness (LSB) galaxies in the Hydra I cluster of galaxies with MUSE at ESO-VLT. The majority of LSB galaxies in the sample (22 in total) are ultra-diffuse galaxies (UDGs). Data acquisition started in December 2021 and is expected to be concluded by March 2024. Up to June 2023, 29 targets were observed and the redshift has been derived for 20 of them. The distribution of systemic velocities Vsys ranges between 2317 km s−1 and 5198 km s−1 and is centred on the mean velocity of Hydra I (Vsys = 3683 ± 46 km s−1). Considering the mean velocity and the velocity dispersion of the cluster (σcluster ∼ 700 km s−1), 17 out of 20 targets are confirmed cluster members. The three objects with velocities of greater than 2σcluster away from the cluster mean velocity could be two background galaxies and one foreground galaxy. To assess the quality of the data and demonstrate the feasibility of the science goals, we report the preliminary results obtained for one of the sample galaxies, UDG11. For this target, we (i) derived the stellar kinematics, including the two-dimensional maps of line-of-sight velocity and velocity dispersion, (ii) constrained age and metallicity, and (iii) studied the globular cluster (GC) population hosted by the UDG. Results are compared with the available measurements for UDGs and dwarf galaxies in the literature. By fitting the stacked spectrum inside one effective radius, we find that UDG11 has a velocity dispersion of σ = 20 ± 8 km s−1 and is old (10 ± 1 Gyr), metal-poor ([M/H] = −1.17 ± 0.11 dex), and has a total dynamical mass-to-light ratio of M/LV ∼ 14, which is comparable to those observed for classical dwarf galaxies. The spatially resolved stellar kinematics maps suggest that UDG11 does not show a significant velocity gradient along either its major or minor photometric axis, and the average value of the velocity dispersion is ⟨σ⟩e = 27 ± 8 km s−1. We find two GCs kinematically associated with UDG11. The estimated total number of GCs in UDG11 - corrected for the spectroscopic completeness limit - is NGC = 5.9−1.8+2.2, which corresponds to a GC-specific frequency of SN = 8.4−2.7+3.2.