It's from Paramount Pictures, and it's referred to as a "personality poster," although I'm not sure whether that's its official title. It's a jumbo lobby card, 14 x 17 inches -- and in addition to its size, what makes it somewhat unusual is that doesn't refer to a specific film, only to Lombard.
Apparently all the studios did something along these lines, particularly those that owned their own theaters, and was a practice that dated back to the teens. Depending upon the manager's whim, they could be hung up or taken down if that particular star's movie was then playing, or it could be displayed semi-permanently along with other notables on that studio's roster. (Many of them were larger than the Lombard poster above, measuring 22 x 28 inches or even bigger.)
But getting back to the Lombard portrait, it's quite well done; double-click on it to view it at roughly full size to completely comprehend its beauty. I'm guessing it was made about 1935 or so.
It's currently being previewed at Heritage Auction Galleries, in preparation for a live auction on July 24 (one week from this Friday). It's valued at $700, with the opening bid at $350. Want to learn more about it, or even bid? Go to http://movieposters.ha.com/common/view_item.php?Sale_No=7008&Lot_No=85762#photo.