The abundance of Li in stars formed within the past 5 Gyr is logN(Li)=3.2(+/-0.2), while the corresponding value for the oldest stars in the Galaxy is logN(Li)=2.2(+/-0.2). The global evidence suggests that the latter represents the full, or the major, part of the primordial abundance, so that the difference of an order of magnitude is due to Li produced in the Galaxy. It is well known that spallation of interstellar CNO by 4He and protons in Galactic cosmic rays (GCRs) can produce Li, but models yield a shortfall of almost an order of magnitude compared with the current observed abundance range. Another GCR reaction, α+α fusion, has been invoked to explain some Li production in the early Galaxy, but application of this to the disk yielded too much early Li or too little current Li. These failures led to a search for alternative mechanisms, essentially stellar, at particular phases of evolution: the helium flash phase in asymptotic giant branch stars, in novae, and in supernovae (SNe). Here we stress the importance of the observed upper envelope in the plot of Li versus Fe in stars as a constraint on any mechanism in any model aiming to account for disk Li. We show that a good match can be found assuming that low-energy GCRs produce the Li, with the α+α reaction as the key mechanism, although production in supernovae cannot at this stage be excluded. There is an apparent time delay in the Li production, relative to O and Fe, which if confirmed could be explained by the origin of a low-energy α-particle component in processes associated with stars of intermediate and low mass. The α-flux at a given epoch would then be proportional to the amount of gas expelled by low- and intermediate-mass stars in the Galaxy, though the acceleration of these α-particles could still be linked to more energetic events as supernova explosions. The present scenario appears to account coherently for the closely related observations of the temporal evolution in the Galaxy (halo+disk) of abundances of 12C, 13C, 14N, 16O, 26Fe, the two main peaks (one in the halo and one in the disk) in the G-dwarf stellar frequency distribution, and the evolution of 9Be and 10B+11B via GCR spallation reactions without requiring the very high local cosmic-ray fluxes implied by the spallation close to SN. Adding a natural mechanism of differential depletion in red supergiant envelopes, we can explain the observed time evolution of the abundance of D and that of the isotopic ratios 7Li/6Li and 11B/10B starting from a standard big bang nucleosynthesis model with baryon density ~0.05. Our model also predicts the second Li ``plateau'' found for [Fe/H] between -0.2 and +0.2, due to the ``loop back'' implied for Li (also for 9Be and B) because of the required infall of low-metallicity gas to the disk. Without ruling out other mechanisms for the main production of Li in the Galactic disk, the low-energy α+α fusion reaction in the interstellar medium offers a promising contribution.