In fact it was Nikon which made the first lenses for Canon initially and also during the Second World War (WWII), the company manufactured binoculars, lenses, bombsights, periscopes and other optical equipment for the Japanese Military.
It was after the culmination of WWII that the company Nippon Kogaku reverted back to manufacturing equipment for civilian use which were all within one factory premises and in 1948 introduced the first Nikon branded camera, the Nikon 1. It had a limited market as it was sold initially within Japan only especially with trade sanctions and other issues the Japanese had to face after the war.
David Douglas Duncan an American photojournalist who was working in Japan at the time the Korean War broke out, was introduced to Nikon lenses by a Japanese photographer Jun Miki. He was the first westerner or probably even the first non-Japanese to use the first Nikon camera and lenses. The popularity of the brand name Nikon gave the impetus for the company to rename itself as Nikon Corporation shedding its former name.
Nikon encountered trade mark issues in Germany with the name Nikon though it was a combination of their previous company, Nippon Kogaku, the German manufacturer Zeiss of the brand “Ikon” saw otherwise. This prompted Nikon to brand their lenses as Nikkor, which still remains so to overcome the problem. Hence if you need lenses from Nikon it would be under the brand name of Nikkor and cameras under the brand name Nikon.