Not a lathe in the true sense of the word, the "Dixie" 'drum lathe' was typical of many similar types from other manufactures. Seemingly a speciality of American makers (the writer knows of only one made in the UK, the recent 2021 "Dynastat" US companies producing or branding them have included Ammco, Barrett, Rels, Kwik Way, Star and Van Norman, etc. Once commonly found in garages and repair shops when automobiles and trucks were fitted exclusively with drum brakes, the first example shown below was manufactured by the "Dixie Machine Division of the Navey Drilling Machine Co. Cincinnti, Ohio". It appears to be of a pre-WW2 design - and might have had a production run from the 1930s to the early 1950s. As often found in products from the incestuous machine-tool world, the Dixie appears to have been built along very similar lines to those sold as the Barrett "Brake Doker" and the Lempco Company's Model 802 - Lempco being a once well-known supplier of garage and workshop equipment and based in Bedford, Ohio. However, both the latter models do have a several differences and what appear to be more sophisticated features and may well have come to market later than the more basic Dixie
Of simple design but robust construction, the Dixie had a built-in electric motor with a V-belt running over 4-step pulleys turning a spindle that may have run in the same type of  Timken taper roller bearing used on the Lempco. As the unit's main job was to clean up the inside surface of a brake drum - no doubt scoured by a neglectful owner running the brakes shoes down to the rivets.- just a single screw-feed cross slide was fitted with a boring bar held in a swivelling toolpost.
In addition to turning, the unit could be fitted with a "honing" or "grinding" kit by which means a much smoother surface could be generated.
One point of interest, the writer not having ever used one, was the inclusion with the Dixie's standard equipment of what the makers described as a "drum damper", this appearing to have been in the form of a wire rope that wrapped around the outside of the drum, so stiffening the assembly and hence - hopefully - helping to ensure a more accurate, parallel cut. Other accessories included with each new example included a range of different diameter arbors to held drums, the necessary cutting tools and a hone.
While, today, the Dixie might find a home in the garage of a vintage car or motorcycle restorer. as drum brakes are still widely used on trucks larger examples of the drum brake lathe are still manufactured. Some, ingeniously, combining the ability to machine both drums and rotors (discs) - the latter fitting employing two parallel cutters that machine both sides simultaneously..