  Lyman break galaxies (LBGs) are promising probes for clustering measurements
at high redshift, $z>2$, a region only covered so far by Lyman-$\alpha$ 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
$83\pm3\%$, for a purity of the selected LBG sample of $90\pm2\%$. This would
deliver a confirmed LBG density of $\sim 620$ 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 $89\pm4\%$ efficiency for $97\pm2\%$ purity.
This would provide a confirmed LBG density of $\sim 470$ 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 $b_{LBG} = 3.3 \pm 0.2 (stat.)$ 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.
