Generally, you say what is on your mind and in your heart. Like a conversation. However, if you are looking for a well-versed prayer, there is a lovely one here.
Indeed, if you are looking for well versed prayers, there are many like the one above, but generally it's the same for most entities, keep calm and be respectful, and just make it like a normal conversation.
Well do not do know of her being a vampire spirit. But someone i read she was known has the mother of all vampires. And some people see her has a demon or a goddness. I do not know why but some people see her has a fallen angel
Lilith Was The First Vampire Created By God According To The Vampire Bible zin The Beginning It Was Lilith And Adam But Lilith Loved The Earth More Than Adam Adam Became Furious And Told God He Wanted A Women Who Would Love Him So God Made Eve Out Of Adams Rib So That She Would Love Him And Lilith Was Banish From Rhe Garden And Became The First Vampire. Some Say She Was Turned By Cain Because Adam And Eve Had Cain And Abel Cain Killed Abel And Was Banished And Left In The Desert It Was So Hot So He Would Hunt At Night Because Of The Lack Of Food And Water He Drank Any Blood He Could His Body Adapted To This And He Starting Forming Fangs And Getting Better Senses And He Created More And More Vampires Him And Lilith.
Basicly Lilith was the first feminist, she refused to lie beneath Adam. Adam wanted a wife who would submit to him, Lilith wanted to be equal. So she was banished and a new compliant wife was made for Adam. Poor Lilith was demonised for her trouble and doomed to have thousands of children.
I do not believe Lilith to be a Demon, men demonized her because she would not submit.