The determination of the observational limit below which the cores of very-low mass objects do not reach high enough temperatures and pressure for lithium destruction is called the lithium depletion boundary (LDB). Up to now, the LDB has been used to derive ages of several open clusters younger than 200 Myr, age considered as the practical upper limit of that method. Here we report on the LDB age of the Hyades, demonstrating that this method can be extended to significantly older ages. We obtained intermediate-resolution optical spectroscopy of seven Hyades L dwarf members with the 10.4-m Gran Telescopio de Canarias. We report a clear detection of lithium in absorption at 670.78 nm in the three coolest and least massive members classified as L3.5-L5.0, whose effective temperatures and luminosities are below 1800 K and -4.0 dex, respectively. We derive a LDB age of 650±70 Myr for the Hyades comparing observational constraints with the state-of-the-art BT-Settl models, in agreement with estimates derived from other methods.