I took Lydia with me and I went over to the Winking Skeever in Solitude, we had an appointment with the steward in Solitude and well...that′s not really part of the story so I'll skip that. Anyway so we went in to the Winking Skeever and I told her to sit down and wait right there. So then I went out and over to Radiant Raiment and got an outfit and dressed up as a bard. I went back to the Winking Skeever and pretended I was just there to have a drink and eventually I made my way over to Lydia and engaged her in conversation, trying to act like we were complete strangers that just met. So I was like "Hey, you come here often?" and "I am from Riften, I am only in Solitude for the burning of the king festival...and...I′ve got a room here at the Winking Skeever for the night..."
But Lydia really didn′t play along at all, she was like "What do you want from me my Thane?" and "Do you want me to carry your stuff?". I am like "No...no, you′re not supposed to act like I am your Thane, I am a bard and you′ve never met me before!". But no, she didn′t get it at all and eventually I just gave up.
So, from my experience, Skyrim doesn't allow for role-playing at all, it was really a big disappointment, I was hoping to spice things up and I was totally let down.