It's from the March 1936 issue of Photoplay, and was taken at the famed Trocadero nightclub in West Hollywood:
The caption reads:
"Frank Fay, Winnie Shaw, Carole Lombard and Bob Riskin think children should be seen and heard too, when they are as cunning and entertaining as little Carol Lee who turned Frank Fay's Vod-vil night at the Trocadero into a riot."
Fay, of course, appeared in two of Lombard's films -- "Nothing Sacred," where he plays the master of ceremonies at a tribute for Hazel Flagg, and "They Knew What They Wanted," where he portrays a rather sanctimonious priest. Shaw was a Warners contract player in the thirties, best remembered for introducing "Lullaby Of Broadway" in "The Gold Diggers Of 1935." She made her last film in 1939, but lived until 1982.
This was probably taken in late 1935 or at the start of 1936, when Lombard and screenwriter Riskin were still "an item." It's sort of ironic to see them in the presence of a child, since Carole wanted to have children and Robert didn't, one of the factors that doomed their relationship. (Another arrived about the time this magazine hit newsstands...some guy named Gable.)
But what of this Carol Lee, who I'm guessing to be about age 9? Whatever happened to her? I wish I could give you a clear-cut answer, but I can't. A check at the Internet Movie Database reveals several people named "Carol Lee," but none fut the time frame. The closest I could find was a Carol Lee who was in the Alice Faye musical "George White's 1935 Scandals," but that person portrayed a chorine, a role the Carol Lee we have in mind clearly wasn't ready for.
So it's possible this Carol Lee never sought a career in movies or show business; if she's still with us today, she'd be in her early eighties...and I bet she'd have wonderful memories of meeting Carole Lombard. Given Carole's smile, the feeling was mutual.