Observations about Ian and Lucy
It seems most people don't think that Lucy's Father had much of an idea that he was her Father - but I think there are some interesting clues that could easily be missed if you haven't watched more than a couple of times that lead me to believe he suspects it - and is guarded about it, too.
First, he is obviously concerned about why she has come - in the scene in the bedroom with Diana he even said "It's very strange". He was contemplating being Lucy's biological Father even then. I don't think he is sure of it yet, but he's definitely thinking about it. Diana got it right that it was Lucy who wanted to come, but Diana doesn't know why. I think Ian is really thinking about it, trying to get his head around it. (I actually think throughout the movie Diana is also processing it, but she doesn't admit it to either him or Lucy - but she's a woman - she senses something is going on.)
Second, notice the timing when he takes Lucy back to the studio to work. Diane and Lucy are washing the dishes, but notice exactly when he interrupts them - it's exactly when Lucy starts to tell Diana about the journal entry/poem her mother wrote. Ian obviously did that on purpose - and it's also reinforced by what Diana says after Lucy goes with Ian - Diana says that he hasn't worked at night for years. I don't think it was an accident that he pulled her from her conversation with Diana. :)
There is serious motivation and depth to these characters - they obviously thought about this as they were creating this story and movie.