Great Old One
If the choice is between species and lineage, for the technical term, I want species.
For the last time, I hope, these are NOT the same thing, never will be the same thing, it's not a question to choose between one and the other. Obviously, species refers to any creature, and there has never been any plan for that to change. And that term will survive because lineage and ancestry would be STUPID to refer to Mind Flayers, or Catoblepas. These are clearly (different) species and because that word does not cause any problem, there is no reason to change it.
The question is ONLY about the current "races" in the game, because of the (annoyingly) negative connotation of that word. The first thing that WotC did, which is clever, is to say that "race" will only ever be used for player characters, which makes sense because at least some of the current races can interbreed. It also avoids the problem of calling all orcs and drows a race, since they have a number of characteristics that offend some people. Note, however, that, as monsters and NPCs, they are species (although it's not technically correct in the biological acception of the word since they can interbreed with other "races", so they are technically not a different species).
But since races only refer to player characters, and WotC was wary about that word, they tinkered with "lineage" (I think Pathfinder uses "ancestry") because PCs are supposed to be exceptional and they could have any parents and ancestors that they want, allowing them to be as mixed as they want and use whatever stats that they want in combination with racial powers of their choice.
Personally, I find this clever from WotC in the sense that it should dilute the "race" problem since people can play anything they want without discrimination, so politically it's a good mood, which by the way seems to have placated most of the people out there who hate the use of the "race" word.
Another good move was to keep it as an option, because honestly, it is clearly power creep and it brings nothing in term of roleplay, it is, technically, purely a powergamer tool since you could, even before that, decide that your character had almost any ancestry that he wanted, as long as you accepted the ASI of the main race that you related to along with its powers.
Which is why I reiterate that, for me, people insisting on floating ASIs are just doing it purely for power, when it has been demonstrated that PCs not using them are perfectly viable. And this is compounded by the fact that people who use it, as far as I've seen in the discussion, don't even bother to explain how their "lineage" got them different ASIs than the standard racial ones, the only justification is that it goes well with their class. Pure powergaming, not an ounce of roleplaying or storytelling there.
Now, contrary to what @Yaarel thinks, Fizban is indeed a significant step, but a significant step BACK, since they totally dropped the use of the lineage word and went back to race (and this after TWBtWL which was already the same, but less significant as it was only an adventure rather than a sourcebook). My take on this is that they are testing the waters, and doing it on races that are not controversial at all, since the outcry seems to have died.
And since Fizban is raising no new outcry (indeed, some people still see it as a step forward towards the elimination of "race" despite all evidence to the contrary), I'm willing to bet that WotC will no longer implement "lineage" moving forward. We will be back to races, although I agree that the new races published don't have fixed ASIs, oply floating ones.
We will see what happens when the next iteration of the game is released in 2 years time, but if you could please stop trying to prove that lineage and species have anything to do with each other, it would be great...