Your “new mutation” example is somewhat flawed; that the babies of both groups produce lactase means that the [genetic] information to do so was present in both groups. Further how do you know that the Europeans weren’t the ‘mutants’ with the common genetic defect of their lactase production?
HGH is an example of something that, in the normal population, dies-off in production after a certain age. Some people have defective “off switches” for their HGH production and so always produce it; a famous person with that condition would be Andre the Giant (The Princess Bride, The Incredible Hulk).
But in both these cases, your lactase example & my HGH example, both groups are STILL human.
Of course they are, but DNA analysis shows the mutation was new at the time, and is just one example of many mutations which happen over time.
Further, the definition of "human" is itself entirely human.
We define ourselves as "human" and consider "human" any bones, fossils or DNA which seem essentially the same as our own.
But bones & fossils have been found of at least two dozen different species of pre-humans dated between us and the early primate fossils.
Some of these are arguably "human" -- i.e., Neanderthals.
Others are clearly more ape-like.
The exact line between "human" and "pre-human" is a matter for scientific analysis and debate.