It's the cover of a 1935 issue of Jueves de Excelsior, the Mexican magazine whose editors put Lombard on their cover on numerous occasions (was she the Jennifer Aniston of her time?).
I don't see the precise date on the cover, but I'm guessing it to be from early May, since one of the stories inside is on the ill-fated Cunard ship Lusitania, presumably to mark the 20th anniversary of its torpedoing by German boats on May 7, 1915 (an event that spurred anti-German sentiment in North America). There's also a Huey Long story inside; he would be assassinated in Baton Rouge, La., later that year. The seller adds there's a boxing story with a picture of Joe Louis, then an up-and-coming heavyweight who wouldn't win the title for another two years.
Aside from a missing page, the magazine is in good condition, If you look closely at the cover, you'll see some writing over Carole's skirt, but that's merely markings, not an autograph. If it were, you can be sure that it would cost a lot more than the $10 price under eBay's "buy it now" policy.
The item will be up until it is sold or just before 4 a.m. (Eastern) on Thursday. If you'd like to buy it, go to http://cgi.ebay.com/1935-CAROLE-LOMBARD-magazine-LUSITANIA-SAN-JUAN-ULUA-/190374601710?pt=Magazines.