> My vague understanding is that you are allowed to enter evidence to impeach someone (show that they are lying) at any time, most notably right after they lied.

In England and Wales, yeah, as long as the other rules are met (it's of value, relevant, not extremely prejudicial to the defendant, not hearsay, etc.)

You wouldn't impeach them though. It could be perjury if they lied under oath, but otherwise it would just be standard discrediting of a given person.

For some reason calling into question the credibility of a witness is generally called impeaching them in common law... never figured out why. Why isn't that the right term here?