I think your guess is in part incorrect?
"Sultry Serenade"was from 1948. But Tyree Glenn played on it, and might well have been responsible for the core riff. But in typical Ellington fashion, he turned a riff into an orchestral piece.
"How Could You Do A Thing Like That To Me" was not recorded until 1954 by Harry James with no lyrics and was credited solely to Glenn:
Here's Tyree's own version from 1962(?)
So if you want to look at "Sultry Serenade" as Ellington's orchestral expansion of a Tyree Glenn"l riff, you would be correct, just as you would be correct in giving Tyree Glenn credit for that riff when it became a stand-alone pop song.
Who that lyricist was, I don't know and probably don't care.