Combined: I've talked to Alvin as much as possible (told him that we are the masters of our own destiny and that he should be a knight rather than a witcher). I've also exhausted all dialogue options available for Berengar, the Lady of the Lake and most other characters in Chapter IV, but nothing seems to help.
Interestingly enough, the "Alvin" quest updates to reflect that I have received the sword, but Paths of Destiny remains at the stage where I'm supposed to wait for the gift.
As for talking to the Lady of the Lake again, as far as I know, she disappears entirely after she hands over Aerondight and I cannot speak to her again.
I realize now that I should have been more specific in my last post. There are actually two gifts that the Lady of the Lake gives you. She gives you Aerondight when you kill Dagon, but BEFORE that, provided that you chose the correct options in the "Paths of Destiny" quest, she will give you some talents you can use to buy abilities. The problem is, she says she will grant you a gift and the game tells you to come back later. So you have to either leave the island and then return, and talk to her again to receive the talents, or you might be able to do it by just meditating at one of the fireplaces on the island and then talking to her again.
So basically, before you fight Dagon, if you leave and return, and talk to the Lady again, there will be another conversation option. She'll grant you some talents, and the "Paths of Destiny" quest will be solved.
At least, that's how it worked for me. If you have a save from before you fought Dagon, load it and try it out and then let me know if it worked.
