  We performed a detailed analysis of the main theoretical uncertainties
affecting the age at the lithium depletion boundary (LDB). To do that we
computed almost 12000 pre-main sequence models with mass in the range [0.06,
0.4] M_sun by varying input physics (nuclear reaction cross-sections, plasma
electron screening, outer boundary conditions, equation of state, and radiative
opacity), initial chemical elements abundances (total metallicity, helium and
deuterium abundances, and heavy elements mixture), and convection efficiency
(mixing length parameter, alpha_ML). As a first step, we studied the effect of
varying these quantities individually within their extreme values. Then, we
analysed the impact of simultaneously perturbing the main input/parameters
without an a priori assumption of independence. Such an approach allowed us to
build for the first time the cumulative error stripe, which defines the edges
of the maximum uncertainty region in the theoretical LDB age. We found that the
cumulative error stripe is asymmetric and dependent on the adopted mixing
length value. For alpha_ML = 1.00, the positive relative age error ranges from
5 to 15 per cent, while for solar-calibrated mixing length, the uncertainty
reduces to 5-10 per cent. A large fraction of such an error (about 40 per cent)
is due to the uncertainty in the adopted initial chemical elements abundances.
