Q: What part does “in wait” play in “lie in wait”? I’d say it’s an adverbial phrase, since it modifies the verb. But then I start to make myself nuts when I consider something like “lie in bed,” where “in bed” is just a preposition and a noun.
A: An adverbial phrase is simply two or more words functioning as an adverb – that is, modifying a verb.
The phrase “lie in bed,” for example, consists of the verb “lie” plus the adverbial phrase “in bed.”
The adverbial phrase here consists of a preposition (“in”) plus a noun (“bed”). It’s a prepositional phrase in itself, but in this sentence it’s also adverbial in that it functions as an adverb would.
Similarly, the phrase “lie in wait” consists of the verb “lie” plus the adverbial phrase “in wait.” The adverbial phrase consists of a preposition (“in”) plus a noun (“wait”).
By the way, the noun “wait” once had more meanings that it does today. For example, it used to mean a watchman or guard.
Today we use it mostly to mean a period of waiting (as in “an hour’s wait”), but something of the old meaning survives in the expressions “lie in wait” (dating from around 1440) and “sit in wait” (before 1300).
In the sense of lying in ambush, English speakers once also used the phrases “lie at catch” and “lie upon the catch.”
A prepositional phrase can also function as an adjectival phrase, as in “They bought the house in the cul-de-sac.” Here, the prepositional phrase “in the cul-de-sac” functions as an adjectival phrase modifying the noun “house.”
Finally, the word “in” isn’t always a preposition. It’s an adverb, for example, in the verb phrase “lie in” (as in, “On Saturdays, I like to lie in,” or “Don’t call before 9, since I’ll be lying in”).