The assumption that the vehicle is a Rolls Royce comes from the repair listed as "replace emblem & plate on RR streamliner". It's true that there was a vehicle called the Rolls Royce Streamliner but this dealership, Hillcrest, didn't deal in Rolls Royces. A closer look at the bill of sale shows the logos for Cadillac and LaSalle. And an even closer look lists the model number of the vehicle as 41-62. The 41-62 is a 1941 Cadillac, Series 62 similar to the one in the image below. And I'm 99.9% sure what was being replaced was the emblem on the rear wheel indicated by the yellow arrow. RR most likely meant Right Rear not Rolls Royce.
But what's most fascinating is my search led me to a page that discusses Gable buying this 1941 cadillac and giving it to his wife, Lombard. This auto and two other Gable cars are owned by The Petersen Automotive Museum, all likely sold by Kay Gable prior to her death.
So all the pieces fit that the bill of sale from Hillcrest Motor Co. settled by the Carole Lombard estate was for a 1941 Cadillac given to her by Gable (seen on the left in the photo below). It was sent in for a repair with a dated bill of January 13, 1942. Did Gable drop it off or his secretary, Jean Garceau? Is it possible Carole took it in the week before? We'll never know but what we do know is that on Tuesday, January 13th, Carole was on the first leg of the bond tour. It's no wonder Gable kept the car. It was her car.