According to the Encyclopedia of Castlevania, Dracula was attracted to her because she resembled his previous dead wife Elizabetha. I don't know how official that is or what the full translation says and the original source web page that mentioned this (KYASSURUBANIA BANPAIAKIRA) has been taken down though (EDIT: though the artwork shown in the above post clearly showed they at least looked alike). I speculate that she was the re-incarnation of Elizabetha as a result.
http://castlevania.wikia.com/wiki/Encyclopedia_of_CastlevaniaDon't know much else about her. She would love Dracula for all eternity... She loved humans and did not want Alucard to do them any harm... Alucard made her some sort of promise as she was dying, but it's not clear what that was (probably made it after Lisa asked him to do humans no harm, but the Succubus's dream sequence really messed up the words she was saying at that point, so we didn't get to hear what Alucard's reply was). Since the Alucard Sword and Alucard Shield were his mother's family heirlooms, she must have come from some sort of warrior or noble family.
Just for fun, here's some more references to Lisa's ill-fated last moments:
According to the synapsis for the upcoming Dracula's Curse animation (non-canon, but could be correct), it was a group of priests and a bishop who led the witch trial that got her burned.
http://www.scribd.com/doc/14077952/Castlevania-DeckAccording to the radio drama, the son of two of the people that Lisa had helped heal (Lyudmil/Ryudomiru) attempted to rescue her from her persecuters, but failed. He later became Alucard's servant and the two of them lived at Dracula's Castle right afterwards (don't know for sure if Lisa ever did though).
http://krizy.livejournal.com/64773.htmlAfter she died, Dracula hugged her closely. Here's a SotN manga advertisement:
http://www.castlevaniadungeon.net/artwork/sotnmanga.htmlEverything else is just speculation. I don't know if the underlings manipulated events to get her killed, but I have suspicions (especially Death) since they might have a big motivation for it.
Why didn't Dracula turn her to a vampire? I suspect he loved her for her purity. Turning her into a vampire would taint her and he would never want that. I suspect they were married, since he and Elizabetha were married, he would probably marry her (though probably not recognized by the church, though I suppose there are plenty of chapels in the Castle he could use if he wanted to). I'd imagine they would still be a couple when she died, for she would love him for all eternity and I suspect he wasn't doing anything "bad" (just Dark perhaps) when they were together.