lower limit vs peak

lower limit and peak both are nouns.

Word	Noun	Adjective	Verb	Adverb
lower limit	Yes	No	No	No
peak	Yes	No	Yes	No

As nouns, peak is a hypernym of lower limit; that is, peak is a word with a broader meaning than lower limit:

Other hypernyms of lower limit include extremum, small indefinite amount, small indefinite quantity.

lower limit (noun)	peak (noun)
the limit on the lower (or southernmost) side of something	a brim that projects to the front to shade the eyes
the smallest possible quantity	the top or extreme point of something (usually a mountain or hill)
	the highest point (of something)
	the most extreme possible amount or value
	a V shape
	the highest level or degree attainable; the highest stage of development
	the period of greatest prosperity or productivity

lower limit (verb)	peak (verb)
	to reach the highest point; attain maximum intensity, activity