Did you actually initiate the quest before meeting Lilith on the road? Because that random encounter spawns even if you didn't talk with Mistress Woolsey. If you got the encounter out of sequence, the quest will never finish properly.
You absolutely must initiate that quest before you first journey outside the Keep.
U have to finish 2 areas then go back to vigils keep. I finished the woods and had the same problem as u. But as soon as I finished the dwarf area, came back to vigils keep and entered the throne room, I got the triggered response from woosley and the quest finished. Maybe that is also required.
I'm drinkin a beer, I'm smokin a swisher I barely can steer, Cause i'm full of this liquor - E40