  The gravitationally lensed quasar J014516.6-094517 at z=2.719 has been
observed with the ESPRESSO instrument at the ESO VLT to obtain high-fidelity
spectra of the two images A and B with a resolving power R=70000. At the
redshifts under investigation (2.1 < z < 2.7), the Lyman forests along the two
sightlines are separated by sub-kiloparsec physical distances and exhibit a
strong correlation. We find that the two forests are indistinguishable at the
present level of signal-to-noise ratio and do not show any global velocity
shift, with the cross-correlation peaking at $\Delta v = 12 \pm 48$ m/s. The
distribution of the difference in velocity of individual Lyman-$\alpha$
features is compatible with a null average and a mean absolute deviation of 930
m/s. Significant differences in NHI column density are not detected, putting a
limit to the RMS fluctuation in the baryon density on $\leq 1$ proper kpc
scales of $\Delta \rho / \rho < 3$%. On the other hand, metal lines show
significant differences both in velocity structure and in column density. A toy
model shows that the difference in velocity of the metal features between the
two sightlines is compatible with the the motions of the baryonic component
associated to dark matter halos of typical mass $M\simeq 2\times 10^{10}
M_\odot$, also compatible with the observed incidence of the metal systems. The
present observations confirm the feasibility of the Sandage test of the cosmic
redshift drift with high-fidelity spectroscopy of the Lyman forest of distant,
bright quasars, but also provide an element of caution about the intrinsic
noise associated to the usage of metal features for the same purpose.
