Lilith is not examined or discussed by professional astrologers .. not even those who are well-versed in astrologers but not actually professional.
In over 45 years of being active in the astrological community, attending seminars and conferences on local, regional, national and even international levels .. not ONCE has anyone brought up Lilith.
The thing about Lilith is that it isn't even an actual body in the heavens .. not like the "planets" (the term includes the Sun and Moon). For that matter, the Nodes (sometimes called the Asc.Nodes) and the Part of Fortune are not actual bodies either. And astrologers don't use these much, either.
I suppose this is just a commercial gimmick by websites. The m
ore stuff they put in, the more "thorough" they appear to those who don't understand astrology. And also, the more stuff they put in, the more the reader is likely to be overwhelmed and buy the website's computer-generated report. However, since the same information is already available for free on both websites and in books, why WOULD you pay for a written report.
For that matter, I only know a few astrologers who use the asteroids. Except for Chiron ... it has been becoming accepted over the past 2-3 decades and I would estimate that about 1/4 of astrologers are now including it in their interpretations.