In basic anyway, the Kobold's were never said to be reptilian (which throws me off still in some other editions):
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Yeah, there were subterranean dog-tiles or some such. Keeping in line with germanic folklore, they could have easily been made into a goblinoid. Part of me likes the weirdness and vagueness of ODD. Pig-faced orcs, elves that wouldn't be recognizable as elves when compared to modern depictions, etc.
In my game I like to use the 5e art and descriptions for what the creatures are really like and use some of the old school art as how ignorant, bigoted peoples of other groups depict them.
Kobolds are one of my favorite species of humanoids in the game, and lizardmen are right up there as well, and I like the current 5e description and lore for them. But I like to think about how a reptilian humanoid with human-like intelligence would actually live and how it would be different from mammalian humanoids. For one, clothing would be more about holding and carrying things or armor in a fight. It would not be for warmth (though more on this below). Also, they would be less concerned with minor scrapes from bushes, rocks, etc. because of their scaly skin, and they would know that minor imperfections will soon be shed away.
But another idea I've played with is to treat some of the reptilian humanoids more like dinosaurs, which were warm blooded, sitting in evolution between reptiles and birds. I can see kobolds and lizard men evolving from a branch of "avian" dinosaurs. Perhaps they are even covered in light features when young, which are shed away when they mature. Looking at them this way allows you to play them a bit more like other playable races. It is difficult to imagine a true ectothermic creature adventuring into the snowy mountains without lots of magic.
I mean, sometimes, the answer is just "magic." Does evolution have much of a place in fantasy setting with gods and magic? Personally, I like to think so, be cause it is fun to think about.