What is the reason for high lithium concentrations in Sun-like stars? In reading the European Space Organisation paper Lithium depletion in solar-like stars: no planet connection (Baumann et al. 2010), several conclusions based on their observations include:


Lithium depletion in Sun-like stars is independent of having planets (an earlier theory), but rather is a function of the star's age.  From the article:



  For solar-like stars, the lithium vs age trends for planet-hosts
  and stars where no planets have been found are statistically
  identical. Thus, the presence of a planet does not influence
  the observed surface lithium abundance.


However, they observed that


  A number of solar-like stars with unusually high lithium
  abundance for their age are present in the field.


and that these stars also have an anomalously low surface gravity.

What is the current theory as to why some Sun-like stars have a relatively high lithium abundance and low surface gravity?
I could offer a couple of speculations - but there is no "theory". Incidentally, I was looking at the refereed journal paper by Baumann et al. (2010).


The atmospheric parameters of these stars are not correct. Given that the ages are derived from the gravities and temperatures of the stars and that the lithium abundances are also dependent on the gravities and particularly the temperatures, there will be correlated errors. I'm actually struggling to understand how you get stars which are "solar analogues", all of which have similar gravities, yet seem to have a spread of ages (estimated from the Teff vs log g plot) from 1-10Gyr? It is notable that there appears to be just 1/117 in Baumann's sample, compared with 10/82 in Israelian's work...
Maybe they are actually PMS stars, so the estimated ages are completely spurious since they assume that the stars are on the main sequence. I would however have expected the abundances to be 3 or higher.


Neither of these explanations seems completely satisfactory.

I mention in passing that the question of planets and lithium is far from settled. The latest salvo in the war was fired by Figueira et al. (2014) who claim there is statistical evidence for enhanced Li depletion in solar analogues with exoplanets.