Abstract: Lyman break galaxies (LBGs) are promising probes for clustering measurements at high redshift, z > 2, a region only covered so far by Lyman-α forest measurements. In this paper, we investigate the feasibility of selecting LBGs by exploiting the existence of a strong deficit of flux shortward of the Lyman limit, due to various absorption processes along the line of sight. The target selection relies on deep imaging data from the HSC and CLAUDS surveys in the g, r, z and u bands, respectively, with median depths reaching 27 AB in all bands. The selections were validated by several dedicated spectroscopic observation campaigns with DESI. Visual inspection of spectra has enabled us to develop an automated spectroscopic typing and redshift estimation algorithm specific to LBGs. Based on these data and tools, we assess the efficiency and purity of target selections optimised for different purposes. Selections providing a wide redshift coverage retain 57% of the observed targets after spectroscopic confirmation with DESI, and provide an efficiency for LBGs of 83±3%, for a purity of the selected LBG sample of 90±2%. This would deliver a confirmed LBG density of ~ 620 deg-2 in the range 2.3 < z < 3.5 for a r-band limiting magnitude r < 24.2. Selections optimised for high redshift efficiency retain 73% of the observed targets after spectroscopic confirmation, with 89±4% efficiency for 97±2% purity. This would provide a confirmed LBG density of ~ 470 deg-2 in the range 2.8 < z < 3.5 for a r-band limiting magnitude r < 24.5. A preliminary study of the LBG sample 3d-clustering properties is also presented and used to estimate the LBG linear bias. A value of b LBG = 3.3 ± 0.2  (stat.) is obtained for a mean redshift of 2.9 and a limiting magnitude in r of 24.2, in agreement with results reported in the literature.