boundary vs lower bound

boundary and lower bound both are nouns.

Word	Noun	Adjective	Verb	Adverb
boundary	Yes	No	No	No
lower bound	Yes	No	No	No

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

boundary: a line determining the limits of an area
lower bound: (mathematics) a number equal to or less than any other number in a given set

boundary (noun)	lower bound (noun)
the greatest possible degree of something	(mathematics) a number equal to or less than any other number in a given set
the line or plane indicating the limit or extent of something
a line determining the limits of an area