We present X-Shooter/VLT observations of a sample of 36 accreting low-mass
stellar and sub-stellar objects (YSOs) in the Lupus star forming region,
spanning a range in mass from ~0.03 to ~1.2Msun, but mostly with 0.1Msun <
Mstar < 0.5Msun. Our aim is twofold: firstly, analyse the relationship between
excess-continuum and line emission accretion diagnostics, and, secondly, to
investigate the accretion properties in terms of the physical properties of the
central object. The accretion luminosity (Lacc), and from it the accretion rate
(Macc), is derived by modelling the excess emission, from the UV to the
near-IR, as the continuum emission of a slab of hydrogen. The flux and
luminosity (Ll) of a large number of emission lines of H, He, CaII, etc.,
observed simultaneously in the range from ~330nm to 2500nm, were computed. The
luminosity of all the lines is well correlated with Lacc. We provide empirical
relationships between Lacc and the luminosity of 39 emission lines, which have
a lower dispersion as compared to previous relationships in the literature. Our
measurements extend the Pab and Brg relationships to Lacc values about two
orders of magnitude lower than those reported in previous studies. We confirm
that different methodologies to measure Lacc and Macc yield significantly
different results: Ha line profile modelling may underestimate Macc by 0.6 to
0.8dex with respect to Macc derived from continuum-excess measures. Such
differences may explain the likely spurious bi-modal relationships between Macc
and other YSOs properties reported in the literature. We derive Macc in the
range 2e-12 -- 4e-8 Msun/yr and conclude that Macc is proportional to
Mstar^1.8(+/-0.2), with a dispersion lower by a factor of about 2 than in
previous studies. A number of properties indicate that the physical conditions
of the accreting gas are similar over more than 5 orders of magnitude in Macc
