lapse vs fall away

lapse is a noun but fall away is not a noun.

Word	Noun	Adjective	Verb	Adverb
lapse	Yes	No	Yes	No
fall away	No	No	Yes	No

As verbs, fall away is a hypernym of lapse; that is, fall away is a word with a broader meaning than lapse:

Other hypernyms of lapse include drop away, drop off, slip.

lapse (noun)	fall away (noun)
a mistake resulting from inattention
a failure to maintain a higher state
a break or intermission in the occurrence of something

lapse (verb)	fall away (verb)
go back to bad behavior	fall to a lower standard
drop to a lower level, as in one's morals or standards	diminish in size or intensity
end, at least for a long time
for time to move forward
pass into a specified state or condition; sink into
let slip