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In astrophysics, the term lithium problem generally refers to a problem more-specifically known as the cosmological lithium problem or primordial lithium problem: astrophysics detects less lithium in the universe than suggested by models of primordial nucleosynthesis. When accounting for the amount of lithium that should result after the Big Bang along with the mechanisms that we can observe that would produce and destroy some, we observe less current lithium than expected.
The oldest observed stars (Population II) appear to have not enough lithium, suggesting by some means it is burned within the stars. Some other stars appear to have too much, suggesting some significant later source. A possible source is cosmic ray spallation in the interstellar medium, i.e., fission produced by cosmic rays. Another possibility is neutrino-induced processes in core collapse supernovae.
The Sun shows a low abundance, seemingly inconsistent with the much larger abundance found in meteorites, this discrepancy termed the solar lithium problem. Both these problems retain research interest.