We apparently have an answer.
The following ad was recently reprinted in the Los Angeles Times blog devoted to L.A. history, "The Daily Mirror":
It ran in the Times of Oct. 5, 1933, and it's promoting the Hollywood premiere of Mae West's new film, "I'm No Angel," and Grauman's Chinese theater on Hollywood Boulevard. And look who's going to be there (specifically, look fifth from the top in the right-hand column):
Yes, Lombard was among those scheduled to be there; I have no idea whether she actually showed up at the premiere. (Someone want to check the papers of that time to find out?) Then again, look at some of the other names listed, and misspelled -- "Katherine Hepburn" (OK, she had only been in films for a year and worked at another studio), "Lydi Roberti" (uh, that was "Lyda"), "Irene Dunn" (hey, where's the "e" in her surname?) and "Marian Hopkins" (poor Miriam...and she was a Paramount star, to boot!). Also note the advertised presence of "Alice In Wonderland" -- we presume that was Charlotte Henry in costume, as Paramount was promoting it as its upcoming holiday blockbuster.
It's certainly easy to understand why so many industry stars and executives, especially those at Paramount, flocked to this premiere. West (shown in a portrait taken by Eugene Robert Richee) had rescued Paramount from possible bankruptcy earlier in the year with the smash hit "She Does Him Wrong" (the premiere of which Lombard had attended, as verified in newsreel footage), and so the studio was pulling out all the stops for this followup. West's good-natured humor about sex, clever writing and musical ability (she had a real feel for the blues) endeared her to Depression audiences.
I'm sure Lombard knew West since both worked at Paramount, but just how well she knew her is uncertain; West had relatively little interaction with other actresses. I would care to guess Carole admired West's comedic approach to sex and her writing ability.
As it turned out, "I'm No Angel" was a big hit as well. Only the strict enforcement of the Production Code in mid-1934 was able to derail West's film career.