In the case of David Byrne and Brian Eno, the answer is: Be themselves.
The music on Everything That Happens Will Happen Today is entirely Brian Eno, while the lyrics are all David Byrne. But in writing words to Eno's music, Byrne's lyrics take on different and exciting dimensions, and in fleshing out the melodies in Byrne's lyrics, Eno's music becomes even more vibrant. They call it "electronic gospel."
And gospel it is. "Everything That Happens" places conundrums ("nothing has changed but nothing's the same / every tomorrow could be yesterday") and stark images ("I saw my neighbor's car explode") against a slow, heavily reverbed background. "One Fine Day" is a pop masterpiece and a cultural-studies dissertation waiting to happen. (Byrne's lyrics were inspired by Dave Eggers' novel What Is the What, and Eno told Rolling Stone's David Fricke that Chris Martin, who had also written lyrics for the song, respectfully bowed to Byrne's version.) "Strange Overtones" is a songwriting master class from Byrne, and the chorus of "Home" sets the oldest, truest folk and blues sentiments to electronic noises. It's transcendent, celebratory and introspective: gospel delivered to a digital world in a digital language.