“Life is a series of natural and spontaneous changes”: did Laozi say it?
Not in the Dao De Jing
No: “Life is a series of natural and spontaneous changes” is not in the Dao De Jing; it shortens Vernon Howard's own account of Taoism in The Mystic Path to Cosmic Power (1967).
Life is a series of natural and spontaneous changes. Don't resist them – that only creates sorrow. Let reality be reality. Let things flow naturally forward in whatever way they like.
The nearest lines in the Dao De Jing
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天下神器，不可为也。
The world is a sacred vessel that cannot be acted upon.
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为者败之，执者失之。
Manipulators spoil it, commanders lose it.
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以辅万物之自然，而不敢为。
He helps the myriad things to be as they are of themselves, and does not dare to act.
Where it comes from
The sentences are in no chapter of the Dao De Jing; Wikiquote lists them among the sayings wrongly credited to Laozi, of unknown origin. Stefan Stenudd, who keeps a list of sayings wrongly credited to Laozi, found a longer form in Vernon Howard's The Mystic Path to Cosmic Power (1967, page 112), where Howard explains Taoism in his own words and does not claim to quote Laozi or Zhuangzi. The shortened form, credited to Laozi, is in Susan Hayward's A Guide for the Advanced Soul (1985), and spread from there. We have not seen either page ourselves.
What the Dao De Jing says instead
Not forcing things is close to the book's thought, though it speaks of the world, not of the changes in one's life. Chapter 29: “The world is a sacred vessel that cannot be acted upon. Manipulators spoil it, commanders lose it.” Chapter 64 ends with the sage who 辅万物之自然: he “helps the myriad things to be as they are of themselves, and does not dare to act.” 自然, “so of itself”, is the nearest the text comes to letting things flow in their own way.