The lobster-eye type of reflective X-ray optics provides a wide field of view and for this reason it can be a convenient approach for the construction of space all-sky X-ray monitors. The hybrid semiconductor pixel device Medipix2 is a single-particle counting detector of ionizing radiation with the photon energy above 3.5 keV. It has small dimensions (256 x 256 square pixels with a pitch of 55 mu m) and low power consumption. The results of preliminary experiments with the Medipix2 detector and the lobster-eye optics are presented and discussed. Tests are performed with X-rays having a photon energy of about 8 keV. The field of view and the spatial resolution are determined. The dependence of the image distortion and the intensity on the source position is investigated.