  Determination of the lithium depletion boundary (LDB), i.e., the
observational limit below which the cores of very low-mass objects do not reach
high enough temperature for Li destruction, has been used to obtain ages for
several open clusters and stellar associations younger than 200 Myr, which
until now has been considered as the practical upper limit on the range of
applicability of this method. In this work we show that the LDB method can be
extended to significant older ages than previously thought. Intermediate
resolution optical spectra of six L-type candidate members in the Hyades
cluster obtained using OSIRIS at the 10.4-m Gran Telescopio Canarias are
presented. The Li~I 670.8~nm resonance doublet is clearly detected only in the
two faintest and coolest of these objects, which are classified as L3.5 to L4
brown dwarf cluster members with luminosities around 10$^{-4}$ solar. Lithium
depletion factors are estimated for our targets with the aid of synthetic
spectra and they are compared with predictions from evolutionary models. A LDB
age of 650$\pm$70 Myr for the Hyades provides a consistent description of our
data using a set of state-of-the-art evolutionary models for brown dwarfs
calculated by \citet{2015A&A..577..42}.
