The quasar in the Hubble Deep Field South (HDF-S), J2233-606 (zem=2.23), has been observed exhaustively by ground-based telescopes and by the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope at low, medium, and high resolution in the spectral interval from 1120 to 10000 Å. The combined data give continuous coverage of the Lyα forest from redshift 0.9 to 2.24. This very large baseline represents a unique opportunity to study in detail the distribution of clouds associated with emitting structures in the field of the quasar and in nearby fields already observed as part of the HDF-S campaign. Here we report on the main properties obtained from the large spectroscopic data set that is available for the Lyα clouds in the intermediate-redshift range of 1.20-2.20, where our present knowledge has been complicated by the difficulty in producing good data. The number density is shown to be higher than what is expected by extrapolating the results from both lower and higher redshifts: 63±8 lines with logNH I≥14.0 are found (including metal systems) at z=1.7, compared with the ~40 lines predicted by extrapolating from previous studies. The redshift distribution of the Lyα clouds shows a region spanning z1.383-1.460 (comoving size of 94 h−165 Mpc, Ω0=1) with a low density of absorption lines; we detect five lines in this region, compared with the 16 expected from an average density along the line of sight. The two-point correlation function shows a positive signal up to scales of about 3 h−165 Mpc and an amplitude that is larger for larger H I column densities. The average Doppler parameter is about 27 km s−1, which is comparable to the mean value found at z>3, thus casting doubts on the temperature evolution of the Lyα clouds.