A possible story of kobolds and dragonborn origin event
Many Generations ago the lizardmen in a jungle region that withered and slowly died.
The lizardmen could no longer survive in the hot harsh sun, and immigrated this led them to a dwarven mountain, to escape the withering heat of the sun, they offered to serve the dwarves of the mountain in return for a place along side the dwarves in the mountain, the dwarves being suspicious allowed only a quarter of the lizardmen in, and they selected only the healthiest and stoutest among the lizardmen, who kept their word and served the dwarves according to mainly dwarven values and eventually gaining full citizenship after playing a crucial role in defending the dwarven stronghold from a orc invasion.
Over time the they came to call themselves dragonborne due to their newfound pride and health with dwarven industry and healthcare but due to their orok heritage, they came to out breed the dwarves in the stronghold, and are now dominant within the stronghold.
Out on the Savannah the rest were at the mercy of the sun, weakend by the loss of their healthiest members, and the sun killing of their biggest members who were hit the hardest by the heat, they marched on eventually stumbling in to a valley with abandoned goblin burrows, it was the shelter they needed and they survived out in the Savannah scavenging what they could scurrying around at night. A changed people and shadow of who they once were, kobolds they became known as by the others in the valley.
In the modern day a dragonborne would hardly accept that kobolds could be relatives, but to the kobolds they are decended from the dragonborne, and gladly tout it as a show of greatness.
I would actually see the 'Kobolds' in this case being at war with the 'Dragonborne'. A blood feud for leaving them in the scorching heat and abandoning their kind for the safety of the mountains. But as is the case in many conflicts/hatreds, the reason is lost in time.
And likely a remnant of the Lizard men, still endure in the vastly redused jungle swamps, consider both traitors of the their kin who feld in the times of troubles in if, perhaps the emmigration and population reduction was what caused the rest to survive.
Who knows perhaps the jungle was "saved" by Elven colonizers who communed with the Genus Logi of the jungle, and helped it recover much of the jungle, saving the remnants of the Lizardmen and imposing some tribal traditions on the Lizardmen to make the Lizardmen live more like the Elves, and all the troubles may well have been blamed on those who left.
And thus a people united in peace and unity , were divided by fate , and seeds of wars was sown.