go down vs lessen

go down and lessen both are verbs.

Word	Noun	Adjective	Verb	Adverb
go down	No	No	Yes	No
lessen	No	No	Yes	No

As verbs, lessen is a hypernym of go down; that is, lessen is a word with a broader meaning than go down:

Other hypernyms of go down include decrease, diminish, fall.

go down (verb)	lessen (verb)
grow smaller	decrease in size, extent, or range
stop operating	wear off or die down
be defeated	make become smaller
be ingested
go under
disappear beyond the horizon
move downward and lower, but not necessarily all the way
be recorded or remembered