I have a project licensed under the LGPL-3.0. A major contributor recently stopped contributing, and is now requesting all their contributions to be removed from the project. All the code in the project is under copyright under the LGPL-3.0. I saw this answer, but it didn’t make it clear for this situation whether the contributor had copyright over their work. Can someone request their code to be removed from a project?
it didn’t make it clear for this situation whether the contributor had copyright over their work
That's because it doesn't need to be made clear - contributors always own the copyright on their work, unless there was a formal copyright assignment to another entity.
However, that isn't the relevant question here. As the copyright holder, they gave you (and everyone else) a license to use their work, and that license is irrevocable - so long as you abide by the terms of the license, you can continue using their work.
Can someone request their code to be removed from a project?
They can request it; you are legally free to ignore it.
Important disclaimer: I don't normally stick the "I am not a lawyer" disclaimer on posts here, because the vast majority of stuff around open source licenses either has actually been upheld in a court of law (in some jurisdictions anyway), or is so close as to be universally accepted to be true as to not be a serious threat. The irrevocability of licenses is not quite at that level; if someone really wanted to argue it, they could probably at least make your life quite painful, and potentially very expensive as well.
This is somewhat complicated since contributing code to a project is not the same as licensing code in a particular manner to the project. Outside of any more explicit agreements, commits to a central public repository can certainly be considered as an understanding that the code will be distributed under the then current project license. In that case, anybody taking the code from the project can "sublicense" that work back to the project under the license they received it under.
Essentially the cat is out of the bag. However, that does not preclude the original author from pursuing legal steps to obtain their goals even though it might ultimately render this pursuit a failure.
The threat of lawsuits is a deterrent that does not fully depend on the ultimate success of such a lawsuit.
So while it is certainly a good idea to know your legal standing, this is only one criterion for picking your next action, and dealing with the situation with a suitable amount of diplomacy may well pay off. You really need to take inventory of how important that contribution may be for the future of the project, how important the goodwill of the past contributor may be, and then offset that with the costs of the hassle your disagreements may cause. And once you know where you want to go, you need to work with the past contributor in the manner that will most likely cause the least damage to your project.