Carole was certainly athletic, but would she have been sufficiently talented in terpsichore to have partnered with, say, Fred Astaire? She might've been able to pull it off, but she clearly would've had to raise her dance game a few notches higher.
George Raft, a fine dancer but obviously no Astaire, was more her speed, and they teamed for two dance films -- "Bolero" in 1934, and "Rumba" the following year. One of the "secrets" of those films was that Raft and Lombard didn't perform some of the more complicated steps; rather, they were "doubled" in those instances by the renowned dance team of Veloz & Yolanda.
Paramount may not have admitted they were subbing for George and Carole at times, but the studio freely admitted they were on hand to give the stars instruction. Take this picture, for instance, showing Lombard with Frank Veloz:
Another photo of the two, used to promote "Rumba," has cropped up, with a blurb on the back saying Carole was being instructed by him:
This latter picture, said to be in excellent condition, is being auctioned at eBay, though you don't have much time to bid on it -- the deadline is 9:45 p.m. (Eastern) tonight. No one has bid on it as of this writing; the minimum bid is $29.95 (a bit steep for some, but this is a rare image). If you're a fan of both Lombard and the dance, this may be for you. To bid or learn more, go to http://cgi.ebay.com/VINTAGE-Carole-Lombard-RUMBA-35-DANCE-INSTRUCT-Portrait_W0QQitemZ350259585226QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item518d1920ca.