“To lead people, walk beside them”: did Laozi say it?
Not in the Dao De Jing
No: “To lead people, walk beside them” is not in the Dao De Jing; the nearest line, chapter 66, says that to lead the people one must put oneself behind them, not beside them.
To lead people, walk beside them.
The nearest lines in the Dao De Jing
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是以欲上民，必以言下之。
So to be above the people, one must speak as one below them;
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欲先民，必以身后之。
to lead the people, one must put oneself behind them.
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太上，下知有之。
The great masters: those below only know they exist.
Where it comes from
We found no source. The sentence is in no chapter of the Dao De Jing, it is not in James Legge's 1891 translation, and Wikiquote's Laozi page does not list it. On Goodreads and other quote sites it opens a passage that goes on with a version of chapter 17: the best leaders barely noticed, then the praised, the feared and the hated, and the people saying “we did it ourselves”. The chapter 17 part is Laozi's; the first sentence is not.
What the Dao De Jing says instead
Chapter 66 has the idea, with a different word. Rivers and seas are kings of the hundred valleys because they lie below them; so 欲先民, “to lead the people”, 必以身后之, “one must put oneself behind them”. Our translation: “So to be above the people, one must speak as one below them; to lead the people, one must put oneself behind them.” The point is humility, the leader who takes the lower and the last place, not companionship. The variant “walk behind them” is close to this line; “beside” is in no line of the book. Chapter 17 adds that the best rulers are those of whom the people only know that they exist.