I know that just about every walk through has suggested that this woman is actually the Daeva in disguise and that it had just killed the victim inside the house (later guarded by a Barcelona soldier). Under normal circumstance, if you try to talk to her, she doesn't answer you but the text shown will indicate that she is frightened and she flees towards the Port District. You cannot catch her nor follow her.

However strangely enough, if you don't say a word, and just walk up to her and "force" combat, you can usually kill her with just one blow and she drops a few coin and you get a few XP for it. You can do this even as a member of the guard walks by and he will do nothing.

http://i184.photobucket.com/albums/x73/ralphrepo/GOG%20com%20games%20images/MysteriousWomanGateDistrict001.jpg

Further, despite the persistent dead body "feature" of the game, her body somehow will disappear. Does anyone have anything more to add to this mysterious woman? I get the impression that she was a part of an incomplete quest thread.

I get the feeling that Lionheart, as a game, was rushed and fairly incomplete because BlackIsle was closing down at that time. I've heard a lot about many incomplete things about this game including Torquemada's divine boon perk which never made it to the final release of the game. And about this lady, nothing seems to come out from it. You can kill her or if you try to talk to her she walks away. You may be right that this may have been another incomplete quest. There is nothing more to this other than you reporting to the guard that you saw a mysterious blue lady near the house and nothing comes out from this too.

I think Lionheart deserves a completed re-release although that sounds impossible :/

*SPOILERS*
My recollections are vague at best sorry, but don't you encounter her at a later quest and she turns out to be an evil Deva? Nothing comes of your first encounter, but it does add some flavour.