The abundance of Li in stars formed within the past 5 Gyr is logN ( Li ) = 3.2 ( \pm 0.2 ) , while the corresponding value for the oldest stars in the Galaxy is logN ( Li ) = 2.2 ( \pm 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 insterstellar CNO by ^ { 4 } He and protons in galactic cosmic rays ( GCR ) can produce Li , but models yield a shortfall of almost an order of magnitude compared with the current observed abundance range.Another GCR reaction , \alpha + \alpha 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 AGB stars , in novae , and during supernova . Here we stress the importance of the observed upper envelope in the plot of Li v. Fe in stars as a constraint on any mechanism in any model aiming to account for disk Li . We show that a good can be found assuming that low energy GCRs produce the Li , with the \alpha + \alpha reaction as the key mechanism although production in supernovae can not 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 \alpha -particle component in processes associated with stars of intermediate and low mass.The \alpha 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 alphas could still be linked to more energetic events as SN 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 ^ { 12 } C , ^ { 13 } C , ^ { 14 } N , ^ { 16 } O , ^ { 26 } Fe , the two main peaks ( one in the Halo and one in the Disk ) in the G-dwarf stellar frequency distribution , and the evolution of ^ { 9 } Be and ^ { 10 } B+ ^ { 11 } B via GCR spallation reactions without requiring the very high local cosmic-ray fluxes implied by the spallation close to SN ( Casuso \& Beckman 1997 ) .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 ^ { 7 } Li/ ^ { 6 } Li and ^ { 11 } B/ ^ { 10 } B ( Casuso \& Beckman 1999 ) starting from an SBBN model with baryon density \sim 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 ^ { 9 } Be 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 \alpha + \alpha fusion reaction in the ISM offers a promising contribution .