Although not "successful", the only one who jumps to my mind is James Fenton.
From wiki: He was the original English librettist for the musical of Les Misérables but Cameron Mackintosh, finding his lyrics uninvolving, replaced him with Herbert Kretzmer; Kretzmer has credited him with creating the general structure of the adaptation. He nonetheless received credit for "additional lyrics" and considerable royalties.
It seems challenging, though certainly not impossible, to make the leap. It seems like the biggest challenge is to make the lyrics simple enough that the information gets across, potentially on only one listening, while the brain also processes the music and the visuals. To me, a poem can luxuriate in greater complexity and depth and stand on its own. Whereas most theatre lyrics, while often clever and even, yes, sometimes poetic, have a huge void when taken apart from their music.