Carole Lombard signed plenty of photos during her career, including the image above, taken by John Miehle. Another inscribed version is for sale at eBay.
Whereas the top photo's inscription is easy to see, the bottom -- in dark ink, under her face -- is far tougher to discern. So I've enlarged it.
According to the seller, it reads, "To Mary and Steve/my best to you both/Carole Lombard". This 9" x 13" photo certainly not as in good shape as the top one; note the 1 1/2-inch tear, as well as a creased service.
This goes for $1,800 straight up (10% off its original price of $2,000) or $75 monthly for 24 months; if neither option suits your fancy, you can make an offer. If you've always wanted a signed Lombard pic, get additional info at https://www.ebay.com/itm/CAROLE-LOMBARD-AUTOGRAPHED-SIGNED-PHOTOGRAPH/283553819062?hash=item42051fe9b6:g:FjoAAOSwDO9dMhmr.