We introduce the Lomonosov suite of high-resolution N-body cosmological simulations covering a full box of size 32 h(-1) Mpc with low-mass resolution particles (2 x 10(7) h(-1) M-circle dot) and three zoom-in simulations of overdense, underdense and mean density regions at much higher particle resolution (4 x 10(4) h(-1) M-circle dot). The main purpose of this simulation suite is to extend the concentration-mass relation of dark matter haloes down to masses below those typically available in large cosmological simulations. The three different density regions available at higher resolution provide a better understanding of the effect of the local environment on halo concentration, known to be potentially important for small simulation boxes and small halo masses. Yet, we find the correction to be small in comparison with the scatter of halo concentrations. We conclude that zoom simulations, despite their limited representativity of the volume of the Universe, can be effectively used for the measurement of halo concentrations at least at the halo masses probed by our simulations. In any case, after a precise characterization of this effect, we develop a robust technique to extrapolate the concentration values found in zoom simulations to larger volumes with greater accuracy. Altogether, Lomonosov provides a measure of the concentration-mass relation in the halo mass range 10(7)-10(10) h(-1) M-circle dot with superb halo statistics. This work represents a first important step to measure halo concentrations at intermediate, yet vastly unexplored halo mass scales, down to the smallest ones. All Lomonosov data and files are public for community's use.