“If you want to keep a friend, never test him.”

Widely attributed to Lincoln, this appears to be derived from Thomas Carlyle's general comment below, but there are similar quotes about Lincoln in his biographies.
Adversity is sometimes hard upon a man; but for one man who can stand prosperity, there are a hundred that will stand adversity.
Thomas Carlyle (1841) On Heroes and Hero Worship.
Any man can stand adversity — only a great man can stand prosperity.
Horatio Alger (1883), Abraham Lincoln: The Backwoods Boy; or, How a Young Rail-Splitter became President
Most people can bear adversity; but if you wish to know what a man really is give him power. This is the supreme test. It is the glory of Lincoln that, having almost absolute power, he never used it except on the side of mercy.
Robert G. Ingersoll (1883), Unity: Freedom, Fellowship and Character in Religion, Volume 11, Number 3, The Exchange Table, True Greatness Exemplified in Abraham Lincoln, by Robert G. Ingersoll (excerpt), Quote Page 55, Column 1 and 2, Chicago, Illinois. ( Google Books Full View https://books.google.com/books?id=JUIrAAAAYAAJ&q=%22man+really%22#v=snippet&)
If you want to discover just what there is in a man — give him power.
Francis Trevelyan Miller (1910), Portrait Life of Lincoln: Life of Abraham Lincoln, the Greatest American
Any man can handle adversity. If you truly want to test a man's character, give him power.
Attributed in the electronic game Infamous
Misattributed

When found, make a note of."
Source: Dombey and Son (1846-1848), Ch. 15

Source: Circle of Flight

As quoted in Extraordinary Lives: The Art and Craft of American Biography (1986) by Robert A. Caro and William Knowlton Zinsser. Also quoted in Truman by David McCullough (1992), p. 44, New York: Simon & Schuster.-
Context: You must be frank with the world; frankness is the child of honesty and courage. Say just what you mean to do on every occasion, and take it for granted you mean to do right … Never do anything wrong to make a friend or keep one; the man who requires you to do so, is dearly purchased at a sacrifice. Deal kindly, but firmly with all your classmates; you will find it the policy which wears best. Above all do not appear to others what you are not.

The Innocence of Father Brown (1911) The Blue Cross
The Father Brown Mystery Series (1910 - 1927)

But the horses didn't want it — they swerved apart: the earth didn't want it, sending up rocks through which riders must pass single file; the temple, the tank, the jail, the palace, the birds, the carrion, the Guest House, that came into view as they emerged from the gap and saw Mau beneath: they didn't want it, they said in their hundred voices 'No, not yet,' and the sky said 'No, not there.'
Source: A Passage to India (1924), Ch. 37

How to Win Friends and Influence People

Source: De Senectute, De Amicitia