“[…] in the New Haven version of the show, Eliza had an additional solo, “Say a Prayer for Me Tonight,” before setting off to the ball, but it was cut during the first week of tryouts. The return of “Just You Wait,” therefore, has all the more impact.”
[...]

“Loewe did not want Eliza to have quite the same kind of romantic number that someone like Gigi sings; the avoidance of such a number is also shown in the removal of the sentimental “Shy” from the score late in the compositional process. Even more strikingly, Higgins refers to Eliza as becoming “my lady” in the unused song “Lady Liza,” a direct nomination of her as his consort. The removal of the long sequence in act 1 (“Come to the Ball,” the ballet, and “Say a Prayer”) was largely due to the running time of the previews in New Haven, but it also served an interpretative purpose. “Come to the Ball” was intensely seductive and featured Higgins persuading Eliza to do his will, again in waltz-time, again with reference to himself as consort (“Come to the ball with me”), while the original lyric for “Say a Prayer” had Eliza singing such sentiments as “If I were a work of art / Would I wake his sleeping heart?” and “Say a prayer that he’ll discover / I’m his lover.” That this material did not make it into the show is no accident.” [...]

“With the exception of the first six lines (which consist of simple verse material), Liza’s opening solo (up to the entrance of the servants) is familiar from the version of the song that made it into Gigi. However, the rest of the lyric is completely unknown:
SERVANTS: Have no fear, you’ll be fine.
LIZA: No, I won’t.
SERVANTS: Gracious, proud and refine.
LIZA: No, I won’t.
SERVANTS: Stately and serene …
LIZA: I won’t …
SERVANTS: Practically a queen …
LIZA: I won’t …
SERVANTS: No, Miss Liza, no, you cannot fail.
LIZA: Fail to end in Reading Gaol.
Oh, how I shall behave …
SERVANTS: No, you won’t.
LIZA: Like I live in a cave.
SERVANTS: No, you won’t.
LIZA: Sit when I should stand …
SERVANTS: You won’t …
LIZA: Shake the butler’s hand …
SERVANTS: You won’t …
LIZA: Future history will write
This was England’s blackest night.
SERVANTS: Don’t worry, Miss Liza … (etc.)
(spoken)
(Servants leave)
LIZA: If I were a work of art
Would I wake his sleeping heart?
Is perfection the only way?
If it is—kneel down—and say
A prayer for me tonight;
That the night will bring
Me ev’rything
I’ve waited for.
Say a prayer that he’ll discover
I’m his lover
For now and evermore.
Pray that he’s lonely, a ship lost at sea;
Searching for someone exactly like me.
And say a prayer that he’ll remember
Long ago somewhere
He said a prayer
For me."

Excerpt From: McHugh, Dominic. “Loverly:The Life and Times of My Fair Lady (Broadway Legacies).”