life-time vs period of time

life-time and period of time both are nouns.

Word	Noun	Adjective	Verb	Adverb
life-time	Yes	No	No	No
period of time	Yes	No	No	No

As nouns, period of time is a hypernym of life-time; that is, period of time is a word with a broader meaning than life-time:

life-time: the period during which something is functional (as between birth and death)
period of time: an amount of time

Other hypernyms of life-time include period, time period.

life-time (noun)	period of time (noun)
the period during which something is functional (as between birth and death)	an amount of time