“Integrity is doing the right thing, even when no one is watching.”

— Clive Staples Lewis

Not found in Lewis's works.
"Integrity means doing the right thing at all times, without hesitation" is found in a 1943 syndicated newspaper column. Elsie Robinson, "Listen, World!" https://www.newspapers.com/newspage/58360960/, Evening News (Harrisburg, PA), 1943-02-24, p. 10.
"Integrity means doing the right thing even when no one is there to judge" is found (unattributed) in the 1965 Journal of Clinical Psychology https://books.google.com/books?id=9rm1AAAAIAAJ&dq=%22integrity%22+%22doing+the+right+thing%22&focus=searchwithinvolume&q=%22doing+the+right+thing%22.
The quote became attributed to C.S. Lewis by 2012 https://books.google.com/books?id=XH-1TURLaf4C&pg=PT154&dq=integrity+%22even+when%22+%22c+s+lewis%22&hl=en&sa=X&ved=0ahUKEwi6x9XznoTKAhUKymMKHdoKCKoQ6AEIHTAA#v=onepage&q=integrity%20%22even%20when%22%20%22c%20s%20lewis%22&f=false.
Misattributed

Adopted from Wikiquote. Last update Nov. 2, 2021. History

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Clive Staples Lewis 272

Christian apologist, novelist, and Medievalist 1898–1963

Jim Stovall (1958) American writer

“Ethical behavior is doing the right thing when no one else is watching — even when doing the wrong thing is legal.”

Aldo Leopold (1887–1948) American writer and scientist

Presumably a paraphrase of "A peculiar virtue in wildlife ethics is that the hunter ordinarily has no gallery to applaud or disapprove of his conduct" or of "Hunting for sport is an improvement ..." above.
Unlikely to be by Leopold, who knew that ethics involves not only doing the right thing, but also determining the right thing in the face of competing desirable criteria.
Misattributed

“A bottom line principle of business—and life—is, to do what is right, even when no one else is looking. Likewise, we ought to do the right thing even if others around us seem to be backwards.”

Don Soderquist (1934–2016)

Don Soderquist “ Live Learn Lead to Make a Difference https://books.google.com/books?id=s0q7mZf9oDkC&lpg=pg=PP1&dq=Don%20Soderquist&pg=PP1#v=onepage&q&f=false, Thomas Nelson, April 2006 p. 145-146.
On Acting with Integrity

“A thing is right when it tends to preserve the integrity, stability and beauty of the biotic community. It is wrong when it tends otherwise.”

Aldo Leopold book A Sand County Almanac

Source: A Sand County Almanac, 1949, "The Land Ethic", p. 224-225.
Source: A Sand County Almanac and Sketches Here and There
Context: Examine each question in terms of what is ethically and esthetically right, as well as what is economically expedient. A thing is right when it tends to preserve the integrity, stability, and beauty of the biotic community. It is wrong when it tends otherwise.