The Vampire Bible states that Lilith met the True Death via the Sun. Then one of her followers gathered her remains and, throught the time, he transported them to many different places until it ended up in that vile in the Authority.
When Godric met the True Death via the Sun, his entire body was incenerated by blue flames and then he turned to ash and blew away in the wind.
When a Vampire meets the True Death via the Sun, their whole body is burned until there is nothing. How is there a vile of Lilith's blood if she burned up in the Sun?