Could you please help me to analisis the sentence structure? Thank you.
The fact that we get to properly end this thing that we all cherish so much we're lucky.

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Ziya's right. There is however a way to make it with what you have. You need to emphasize "we're lucky" part, that'll add some dramatic effect. "The fact that we get to properly end this thing that we all cherish so much... we're so lucky.". Read this in a Christian Bale voice from American Psycho, you'll get what I mean ;) 
https://www.youtube.com/watch?v=0S7olzuojGY

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Thank you so much Ziya.

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One little correction...analyse (with a Y).

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One more thing...there is a Y in analyse.

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Your sentence isn't quite complete. You need to add something.
The fact that we get to properly end this thing that we all cherish so much SHOWS/MEANS/MAKES US REALISE we're lucky.

The fact means we are lucky.
What fact? That we get to properly end this thing.

What thing? The one that we all cherish.

How much do you cherish it? So much.