Dur-O-Lite was founded by John Lynn, one of the founders of Autopoint, sometime shortly after 1925, when a business disagreement led Lynn to sell his interest in Autopoint. According to promotional materials printed around 1934, Lynn "conceived the idea of a plunger type pencil, with the tip removable from the barel while in active service in France . . . after the war, [he] organized a Company to manufacture a similar pencil, and later designed the DUR-O-LITE, and organized this company."
This disagreement is the reason early Dur-O-Lites closely resemble early Autopoints, and the reason the two companies remained bitter rivals for decades after.
(click on pictures to enlarge)
Early Dur-O-Lites strongly resembled Autopoints in every respect except for colors and the clip. The mechanisms were nearly identical to Autopoints.
A few years ago I had a green and black early Dur-O-Lite with a cigarette lighter built into the cap. Oh why, oh why did I let that one go!
Keenpoint was a subbrand of Dur-O-Lite, as the bottom 2 examples clearly indicate.
However, the top example is a bit unusual. It is marked "Keen Point Chicago" on the metal top and is identical to pencils produced by National (under the Diamond Medal name, among others). It is clearly a National Pen Products model.
Whether Dur-O-Lite contracted with National to produce some Keen Points, or whether Keen Point was a stand alone company that was later acquired by Dur-O-Lite, is the subject of continuing research.