as luck would have it vs fortunately

as luck would have it and fortunately both are adverbs.

Word	Noun	Adjective	Verb	Adverb
as luck would have it	No	No	No	Yes
fortunately	No	No	No	Yes

As adverbs, as luck would have it and fortunately are synonyms defined as:

Other synonyms of as luck would have it include fortuitously, luckily.

as luck would have it (adverb)	fortunately (adverb)
by good fortune	by good fortune