Just out of interest, how can one tell the difference between primordial lithium and lithium that is manufactured through stellar nucleosynthesis?
I'm not Wrangler, but I hope you won't mind me jumping in with a (very) brief answer ...
A: with considerable difficulty!
Not only is 7Li generated by BBN (Big Bang Nucleosynthesis), but it is also generated in stellar nucleosynthesis. However, it is also destroyed in stellar cores, so its observed abundance, due to this process, must come from somewhere else. There are several sources, such as flares, novae, and AGB stars; supernovae are also expected to produce some.
But wait! It gets more complicated!!
When a high energy particle collides with the nucleus of an atom such as C or O - which are not rare in the interstellar medium (ISM) - the products include 7Li. This process is called spallation, and as the ISM (and the IGM - inter-galactic medium) has plenty of high energy particles passing through it (they're called cosmic rays, or, rarely today, galactic cosmic rays), 7Li will be produced.
So, three+ sources, and two+ sinks (spallation also destroys 7Li).
However, the other stable Li isotope (6Li) is different: no BBN source, very small source in stars (flares), and prolific cosmic ray spallation source. Sinks are the same, except that for 6Li, destruction in stars is even more efficient than for 7Li.
The principal method of estimating primordial Li abundance is interpretation of the spectra of 'low metallicity stars' (stars with low abundances of 'metals'- astronomers call all elements other than H and He 'metals') - the 7Li in them is assumed to be primordial, once a correction for the contribution of ancient cosmic ray spallation is added (estimated from the abundance of 6Li in such stars) ... metal-poor stars are very old, they formed from gas which had been only slightly enriched with metals, from earlier generations of stars).
Needless to say, there is a great deal of astrophysics involved in this conclusion, not to mention the uncertainties of estimates of both 6Li and 7Li in the spectra of faint stars!
The logic chains, and the astrophysics, have been checked, tested, independently verified, etc, etc, etc six ways to Sunday, and the conclusions (concerning primordial 7Li abundance) seem to be quite consistent. However, given some of the uncertainties, it is premature to say the conclusions are robust (IMHO). For example, the ratio of 6Li to 7Li produced by cosmic ray spallation depends on several factors, and extrapolating from what today's cosmic ray energy spectrum is to that of the time when the old stars we observe were accumulating 6Li may be an extrapolation too far (IMHO).