hang back vs lag

hang back is not a noun while lag is a noun.

Word	Noun	Adjective	Verb	Adverb
hang back	No	No	Yes	No
lag	Yes	No	Yes	No

As verbs, lag is a hypernym of hang back; that is, lag is a word with a broader meaning than hang back:

Other hypernyms of hang back include dawdle, fall back, fall behind.

hang back (noun)	lag (noun)
	the act of slowing down or falling behind
	one of several thin slats of wood forming the sides of a barrel or bucket
	the time between one event, process, or period and another

hang back (verb)	lag (verb)
to lag or linger behind	throw or pitch at a mark, as with coins
	cover with lagging to prevent heat loss
	hang (back) or fall (behind) in movement, progress, development, etc.
	lock up or confine, in or as in a jail