Lithium is hard for a star to produce. Stars fuse hydrogen into helium because that is the reaction that happens first, at the lowest temperature and pressure. While these reactions are ongoing, you have both hydrogen and helium in your fusion region, but the temperature is not high enough to fuse lithium. The star will entirely consume its hydrogen supply before the temperature and density get high enough for lithium fusion.

But then once the temperature is high enough for lithium fusion, there's only helium available! You can't make lithium out of two helium 4 nuclei. You can make beryllium 8, but beryllium 8 is unstable. If you only have helium 4 to work with, the next stable thing you can make is carbon 12. So, Li, Be, and B get skipped.

Stars do make small amounts of these elements, but they're on awkward side chains that are much less common than the direct, no funny funny business main reaction chain. Also, Be and B appear as intermediate products during some hydrogen fusion chains, but they don't stick around very long.