lower limit vs extremum

lower limit and extremum both are nouns.

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

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

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

lower limit (noun)	extremum (noun)
the limit on the lower (or southernmost) side of something	the point located farthest from the middle of something
the smallest possible quantity	the most extreme possible amount or value