Mr. Gilmore, the notorious spree-killer, uttered the words “Let's do it” just before a firing squad executed him in Utah in 1977. Years later, the phrase became the inspiration for Nike's “Just Do It” campaign. ... Dan Wieden, who first realized that a slight tweaking of Mr. Gilmore's last words might make a good slogan for athletic gear, said the resonance of “Just Do It” was completely inadvertent and unforeseen. “I like the ‘do it' part of it,” Mr. Wieden, a co-founder of Wieden & Kennedy, says in the film, recalling the moment it dawned on him to use the phrase. “None of us really paid that much attention. We thought, ‘Yeah. That'd work,' ” he says, adding, “People started reading things into it much more than sport.”