A question about the show:
Do they touch on the part where Lara and Pasha are talking in Pasha's room and Yury walks past in the street and sees the small circle the candle burns in the ice that coats the window? That instance is probably one of the most important bits in the book and I'm curious if the include it.
Thought I'd just expand on the comments above - I've been away so only just saw your question!
As everyone has said, they don't, unfortunately. I missed it being in the show the first time I went, but when I saw it the second time (and third and fourth!) I felt it didn't detract from the storyline at all because they have Yury noticing her in the street on two occasions early on.
Firstly, Yury begins the song "Who is She" just after she tries to shoot Komarovsky. When he overhears her and Komarovsky arguing he is instantly drawn to her to find out what passion drove her to do it. When Lara leaves he challenges Komarovsky and they argue and Komarovsky threatens him.
Two years later she marries Pasha and sings "When the Music Played" which tells Pasha about her affair with Komarovski. Pasha immediately runs away and Lara goes out into the street and is waiting for him in the rain. Yury sees her and begins to talk to her, while covering her with his umbrella, and asks why she shot Komarovski. When she leaves him he continues to sing the last verse of the song as he watches her go.
Then she meets him years later on the front and says how wonderful it is that he portrayed Russia so passionately in the poem "Waiting in the Rain" but he tells her the poem is actually about a woman he saw standing in the rain. She comments that she must be a remarkable woman to make him feel so much and he agrees with the words, "She is."
So the way I see it, even though it's not as the book has it with both of them so close but so far away as he passes under the window, the musical combines the importance of that first moment of him noticing her without her being aware of him when he sings the song "into the wind" (my imagination in inverted commas) and then later when he writes the poem because of the effect she had on him. To me, the fact that the song continues after two years, even though he hadn't met her up until this point in time, is just confirmation of his never having forgotten her and that his longing has never ceased.
Here are the words to the song "Who is She" by Amy Powers and Michael Korie, which I believe show Yury's longing behind the words.
"A girl walks in, she shoots a gun ... who is she?
She doesn’t cry, she doesn’t run ... who is she?
What clouds her pretty face with hate?
What brought her to this fevered state?
To shoot a royal magistrate ... who is she?
She seems to know him far too well ... why would she?
As if she holds him in some spell ... why should she?
Too young to need a man like that
A crass, conniving bureaucrat
Alas, is this a lover’s spat ... how could she?
The blaze in her eyes ... a storm on the rise ... defiant and daring.
How wondrous the thrill ... to follow your will ... without even caring.
A criminal evades arrest ... how does she?
She flees the scene and none protests ... who was she?
The orchestra resumes the beat
The servants pour Château la Fête
She fades into a winter street ... and no one seems to care.
Who is she? Was she ever there?
The branches of the moonlit trees conceal her
Yet somehow in a sudden breeze I feel her.
A touch of danger in the air
Invisible but everywhere
Then gone ... a moment that is bare ... a shadow on the snow.
The drama has passed ... it’s quiet at last ... no storm in the making.
So why do I stand ... stills clenching my hands ... to stop them from shaking?
Who is she? Who is she? Who is she?
A touch of danger in the air ... invisible but everywhere
Who is she?"
At the end of the book I think you mean the reference "To the two aging friends sitting by the window it seemed that this freedom of the spirit was there, that on that very evening the future had become almost tangible in the streets below, and that they had themselves entered that future, and would, from now on, be part of it." I think that theme is taken up by the finale of the song "On the Edge of Time" when it says:
"Ensemble: "...breathing in your spirit.
Though my heart is frail and death will come, I no longer fear it.
Nations rise and fall, triumphs come and go ...
Yury: I know when life is through, my love will live in a ray of light ...
Lara: ... in a distant chime ...
Both Yury and Lara: ... on the edge of time with you."
So I see it as the "ray of light" which Yury sings about above, is the window with the candle melting the ice that you refer to, and that the "entered that future" from the book is the two of them singing how their love will live in the light and in the chime forever together.
Probably a very poor interpretation but maybe that helps a little - and if not - I've just taken up too much of everyone's time - sorry!