Lithium is actually consumed in the cores of stars, so generally they have low Lithium content. (Lithium is manufactured by supernovae and was generated in small amounts in the Big Bang, so there is SOME in the Universe, but it keeps getting used-up in stars)

If a star is found with significant amounts of Lithium, one explanation is that it has swallowed a planet or two in the not-too-distant past, and hence the assumption is that it has had a rather unstable planetary system.

Low-Lithium stars are more likely to have had a long stable existence and burned-up their original Lithium supply.