Currently, the standard cosmological model faces some tensions and discrepancies between observations at early and late cosmological time. One of them concerns the well-known H0-tension problem, i.e., a ∼4.4σ-difference between the early-time estimate and late-time measurements of the Hubble constant, H0. Another puzzling question rests in the cosmological lithium abundance, where again local measurements differ from the one predicted by Big Bang Nucleosynthesis (BBN). In this work, we show that a mechanism of light dark matter production might hold the answer for these questions. If dark matter particles are sufficiently light and a fraction of them were produced non-thermally in association with photons, this mechanism has precisely what is needed to destroy Lithium without spoiling other BBN predictions. Besides, it produces enough radiation that leads to a larger H0 value, reconciling early and late-time measurements of the Hubble expansion rate without leaving sizable spectral distortions in the Cosmic Microwave Background spectrum.