For one thing, any Population III star of 0.8 to about 2 solar masses most likely would have long ago gone Nova leaving behind white dwarf. Those could be hard to find, even if we knew where to look.

Good luck finding a Population III object of .1 solar masses or less. Red dwarfs and brown dwarfs are hard enough to detect within only a few light years.

As telescopy gets better and better, I await more surprises.

There’s more: cosmic rays. These can both create and destroy Li, so estimates of the amount of Li in Pop II stars needs to factor in what – it has always seemed to me – an unknown that we have essentially no handle on; namely, the “cosmic ray” spectrum, and its evolution, from the end of BBN to the formation of the Pop II stars whose spectra we observe today. My reading of the relevant literature is that this is rarely even mentioned, much less modeled in a robust way.