peak vs lower limit

peak and lower limit both are nouns.

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

As nouns, lower limit is a hyponym of peak; that is, lower limit is a word with a more specific, narrower meaning than peak:

Other hyponyms of peak include minimum, maximum, upper limit.

peak (noun)	lower limit (noun)
a brim that projects to the front to shade the eyes	the limit on the lower (or southernmost) side of something
the top or extreme point of something (usually a mountain or hill)	the smallest possible quantity
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

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