After Memory Block 1
After it is suggested your character get some rest, both lucy and the doctor will walk back in the room, then the doctor leaves, leaving lucy alone with you.
1st Interact:
Lucy and Desmond talk about Desmonds past, his parents and his likeness wth Altair.
2nd interact (As she's walking away):
Desmond wonders how he was found by Abstergo, and Lucy informs him it was probably his drivers liscense.
3rd interact/4th Interact (While she is back at her computer):
These 2 interacts loop over and over, and are just 2 comments; ''Arent you tired?'' and ''Can't talk, gotta work''
After Memory Block 2
After the first assassination you're released from the Animus and the doctor walks from the room leaving Lucy in a chair alone.
1st Interact:
Desmond asks Lucy to emphasise with him and tells her he thinks the whole situation is screwed up, and they also talk about the deadline Lucy and the doctor have.
2nd Interact:
Lucy explains the translation to modern day tongue using the animus.
3rd Interact:
Lucy talks about Abstergo.
4th/5th Interacts:
Again these are just loops of ''Cant talk, gotta work'' and ''Arent you tired?''.
After Memory Block 3
After assassinating the second target of block 3, the block will finish and you will be returned to the Animus room where, as it turns out, the Animus has overheated. The doctor will leave the room leaving you alone with Lucy.
1st Interact:
Desmond and Lucy talk about how the Animus was created, and Lucy mentions something about the doctor saving her life.
2nd Interact:
Lucy speaks of how, after she helped oversee the construction of the Animus, 3 men kidnapped her and said she was going to die; then Vidic saved her and she has been a 'prisoner' of Abstergo ever since.
3rd/4th Interacts:
Yet again, loops of ''Cant talk, gotta work'' and ''Arent you tired?''.
After Memory Block 4
After exiting the Animus it appears the Assassins have come to try and break you out of Abstergo's hold. Lucy and you talk for some time about how Abstergo is actually a company created by the templars and they are not actually a thing of the past, and Lucy leaves the room.
NOTE: There is no interactive dialogue after this memory block. There is a lot of story dialogue but none of it is interactive. If you try to follow Lucy to the room door in the hopes of interacting with her for dialogue, she will just stop and say things such as 'I cant leave until you're in your room', however this does not count towards the achievement.
After Memory Block 5
After exiting the Animus, Vidic tells you (or Lucy, not sure) that he has work to do, and that you (or Lucy) has the night to themselves. When Desmond gets up, go and interact with Lucy.
1st Interact:
Lucy tells Desmond that if Vidic and his superiors manage to access Desmonds last memory, they will use it to find the piece of eden and control everyone on earth to co-exist in harmony. Lucy gets a phone call, and walks over to Vidics computer.
2nd Interact:
Lucy talks about how there are more than just the one piece of eden and that Abstergo are trying to locate them using Desmonds memory, then Vidic phones here impatiently about Desmond's files.
3rd Interact:
Lucy talks about how an accident occured at any underground facility by Denver international airport.
4th/5th Interacts:
Once again, loops of ''Cant talk, gotta work'' and ''Arent You tired?''
After Memory Block 6
After taking your leave of now-dead Robert, you exit the Animus to sounds of gunfire and after some talks with Lucy and Vidic, it seems the threat has been neutralised and the assassins who came to free Desmond are dead. Vidic leaves the room telling Desmond to rest up and Lucy sits on the Animus, which is when she can be spoken to.
1st Interact:
Lucy Apologises to Desmond and Desmond expresses his anger over the whole situation, worrying about his parents. Lucy shows him that she's not quite who he thinks she is, and the dialogue ends.