A “lie-in” means the practice of resting (either awake or asleep, I believe) while lying down. The OED’s earliest citation is 1867: “The luxury of ‘a long lie in’, is the earliest and most universal of the delights of a working man’s Sunday.” A comparable term is “lie-down.”
They are two of a number of British expressions formed by making nouns out of phrasal verbs; other examples are “fry-up” and “carve-up.” The British also noun-ize some simple verbs that Americans do not, as in “having a sleep” and, indeed, “having a lie.”
Lynne Murphy’s Facebook friend notwithstanding, I don’t see any of these catching on in the U.S. and so, for the time being, categorize them as “On the Radar.”
Update: As commenters were quick to point out, my definition of “lie-in” was seriously wanting, specifically omitting the key element of staying in bed longer than one would normally do, without actually being asleep. It strikes me that this may be a bit of cultural difference that goes beyond language. That is, Americans don’t use “lie-in,” or have our own equivalent, is that we so rarely engage in this practice.