“When I let go of what I am, I become what I might be”: did Laozi say it?
Not in the Dao De Jing
No: “When I let go of what I am, I become what I might be” is not in the Dao De Jing; the nearest lines are the opening of chapter 22, “The bent is made whole”, and chapter 48 on losing every day.
When I let go of what I am, I become what I might be.
The nearest lines in the Dao De Jing
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曲则全，枉则直，
The bent is made whole, the crooked is straightened,
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洼则盈，敝则新，
the hole is filled, the worn-out is renewed,
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少则得，多则惑。
with few there is attainment, with much there is confusion.
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为学日益，为道日损。
Pursuing learning, one gains every day; pursuing the Way, one loses every day.
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损之又损，以至于无为。
Losing and losing again, one arrives at non-action.
Where it comes from
The sentence is in no chapter of the Dao De Jing, and Wikiquote's Laozi page does not list it. Stefan Stenudd, who keeps a list of sayings wrongly credited to Laozi, traces it to page 43 of John Heider's The Tao of Leadership (1985) and says it is very loosely based on the first lines of chapter 22. We have not seen the 1985 page ourselves. The Chinese text has no “I” who lets go of a self.
What the Dao De Jing says instead
Chapter 22 opens with reversals: “The bent is made whole, the crooked is straightened, the hole is filled, the worn-out is renewed.” They describe how things go, not a choice to give up who you are. The idea of losing to gain is plainer in chapter 48: 为道日损, “pursuing the Way, one loses every day”, until one arrives at non-action.