I don’t really get deep into compatibility questions “for free” because they are so common. I have literally hundreds of questions in my inbox just like this and I couldn’t possibly explain the nuances of all those relationships on this blog in this current version of my lifetime…
But regarding Lillith…
You should be aware Lillith works as a trifecta of sorts. There are 3. (For those who believe in Lilith anyway, which I do) Which Lilith conjuncts your Venus and is the conjunction within 5 degrees? If not it won’t really matter.
Also, Lilith represents kind of a female Plutonic energy. So basically its a person’s scary sexy bitchy side. So if your Venus conjuncts his Dark Moon Lilith you may bring out a real bitter and insecure part of him. He may feel jealous of your feminity or want to take advantage of it in some way. He may be obsessed with you in like a love/hate kind of way. Your femininity may bring out insecurities about his own feminine side. (Think the wicked witch of the west)
If your Venus conjuncts his Black Moon Lilith, your femininity may bring out his really sexy psychedellic side. He may reach sexual peaks with you and go into really deep sexual trances. He may get really into the occult and start exploring his dark and mysterious sides with you. Maybe try psychedellic drugs or witchcraft (think black magic woman).
If your Venus conjuncts his Asteroid Lilith then you may be like teenage best girlfriends dying your hair green together and making weird art. Your feminity may bring out a more rebellious but less sexual side of him. You may bring out his inner feminist that wants to change society and bring the ruckus but is quite inexperienced and naive in many ways. (think joan of arc).
Lilith is pretty complex and it usually makes sense to look at how all 3 work together and which one is in the strongest position in an individual chart. That will tell you the most about how it will work with compatibility.