For the Conversationalist achievement you need to talk to Lucy after every time you wake up, until she tells you "I think you should go lay down" or something along the lines of that statement.
Here's a breakdown of the conversations to make sure that you have :
AFTER Memory Block 1 (this is after you drop the logs from the tower):
Desmond - "ran away from farm"
Desmond - "motorcycle license" (talks about how they found Desmond, by running name through DMV)
Memory Block 2:
Lucy : "we have a deadline"
Desmond : "why do they talk like they're from the future?"
Desmond : "Tell me more about Abstergo"
Memory Block 3:
Desmond : "why's he always yelling at you?"
Desmond : "what do you mean, you're a prisoner?"
[This is where you go into your room, DONT go to bed. Get access code from closet that is now open. Go to sleep, wake up next morning, and walk up behind the doc while he's standing facing the window. This is when you steal his pen so you can access computers]
Memory Block 4:
Lucy : "assassins coming to rescue you"
[Go to your room, DONT sleep, instead turn around and get out of your room. Go check computer and read all the emails. now zzzzzzz]
Memory Block 5:
Desmond : "problem with the animus"
Desmond : "using me to find the templar treasure?"
Desmond : "what's that mean, everything's Denver?"
[Go to room, dont sleep, check for more emails]
Memory Block 6:
Lucy : "I'm sorry Desmond" (Achievement unlocked after this lengthy dialogue)