The Lilith Fund is a real thing helping people to get abortions.
From the about page at LilithFund.org:
What Does Lilith Fund Do?
Lilith Fund assists Texans in exercising their fundamental right to abortion by removing barriers to access. Lilith provides direct financial assistance to empower people seeking to terminate an unwanted pregnancy, and education and outreach within the community about reproductive rights.
There's also a page about it at AbortionFunds.org.
This organisation isn't universally known - it operates specifically in the US state of Texas. But Simone Kern lives in Texas, so they likely would have heard about it (they also follow it on Twitter).
Why the connection between Lilith and abortion, though?
Maybe "The Lilith Question", an article in another organisation (this time a magazine) named after Lilith, provides some clues:
The most ancient Biblical account of the Creation relates that God created the first man and the first woman at the same time. Jewish legends tell us that this woman was Lilith.
Lilith, we learn, felt herself to be Adam’s equal (“We are both from the earth”) but Adam refused to accept her equality. Lilith, determined to retain her independence and dignity, and choosing loneliness over subservience, flew away from Adam and the Garden of Eden.
For this reason, Lilith is sometimes used by feminists (especially Jewish feminists) as a symbol of a strong independent woman who wants to do her own thing. More information on that connection may be found at Ann R. Shapiro, "The Flight of Lilith: Modern Jewish American Feminist Literature", Studies in American Jewish Literature 29 (2010), pp. 68-79.
I can't find any direct currently visible evidence that Simone Kern is Jewish, but their Twitter bio says "feminist" and used to put Jewish there too (or so Google search previews are telling me), and apparently Kern grew up in a Jewish family. A Jewish feminist writer would likely be aware of the cultural connotations surrounding Lilith.