Here's Carole Lombard, "Paramount star," as part of a display board for Max Factor lipstick. But in the 1930s, stars' agents didn't make deals to advertise products -- stars' studios did. This was evident in a contract Lombard signed with Factor on July 13, 1932:
As you can see, Paramount was clearly in control of the process; Carole simply signed the one-year ad deal engineered by the studio. A page from January 24, 1975, confirms its veracity:
eBay promoted this item slightly more than a year ago (https://carole-and-co.livejournal.com/896050.html), and the asking price was $2,800, the same sum it's being offered for now (or you can make an offer). Moreover, it has a certificate of authenticity.
If interested, visit https://www.ebay.com/itm/CAROLE-LOMBARD-DOCUMENT-SIGNED-07-13-1932/303126503425?_trkparms=aid%3D111001%26algo%3DREC.SEED%26ao%3D1%26asc%3D20160811114145%26meid%3D2e656e2c9f224f8488ac79b25e0aa588%26pid%3D100667%26rk%3D1%26rkt%3D8%26sd%3D303126503425%26itm%3D303126503425&_trksid=p2045573.c100667.m2042 for additional information.