Reason for different pronunciations of "lieutenant"

Solution 1:

Etymonline indicates that spelling with lef- dates to the 14th century, but that the origins of that spelling (and presumably its associated pronunciation) are “mysterious”. The word comes originally from Old French, and according to the OED, Old French replaced word- and syllable-final [w] with [f]; for the Modern French word lieu, this is shown by an Old French spelling variant luef. Both forms, whyever they exist, just happened to stick.

Solution 2:

'Lieutenant' comes from French lieu ('place') and tenant ('holding'). Some sources claim that 'lieutenant' had alternative spellings such as leftenant, leftenaunt, lieftenant, lieftenaunt etc., and that the ModE pronunciation with /f/ (BrE mostly) is a holdover from those spellings.

I thought the pronunciation with /f/ arose from the 'minim confusion'; in Middle English, both v and u were used interchangeably. According to Lexico, "the u at the end of Old French lieu was read and pronounced as a v, and the v later became an f". I can see how the v became [f] (see 'assimilation') so it sounds plausible to me. However, according to Etymonline, the OED rejects that theory.

The ModE pronunciation with /f/ means one of the following things:

1. The speakers of the French dialect lieutenant was borrowed from probably pronounced the ⟨u⟩ as [v] in some places and it took the devoicing from the following /t/ (cf. 'hafta' from have to)

2. Or, as orthographic ⟨u⟩ and ⟨v⟩ were often used interchangeably, Anglophones for some reason hypercorrected their pronunciation to match the orthography, so: /l(j)ɛu:ˈtenənt/ (or /l(j)ewˈtɛnənt/) → /l(j)evˈtɛnənt/ (hypercorrection) → Assimilation → /l(j)efˈtɛnənt/.

3. Or, the Anglophones confused the lieu with the English word leave (live) as and got the pronunciation /l(j)evˈtɛnənt/ instead of /l(j)uːˈtɛnənt/ and then later on the /v/ got devoiced to /f/

4. Or, the pronunciation with /f/ is a holdover from one of the spellings with an orthographic f

5. Or, the /v/ was epenthetic (cf. Modern French pouvoir from pooir). This can be confirmed at Wikitionary. But it seems less likely.

According to More Word Histories and Mysteries: From Aardvark to Zombie (American Heritage Dictionary), the origin of the pronunciation with /f/ “is not known with any certainty, but similar pronunciations are attested in Middle English times by such spellings as leuftenant, luffetenand, and levetenaunt”. Note the spelling with f and v.

The Old French word lieu had a rare variant form luef, and a form of Old French lieutenant using this rare form rather than lieu may have been picked up by Middle English speakers. In addition, the Old French pronunciation of the word lieu was something like (lyĕw), although this has developed into (lyœ) in Modern French. It is possible that Middle English speakers may have heard the final (w) of this word [...] as a (v) or (f) [...].

Both [v] (also [f]) and [w] are ‘labial sounds’—that is, made with the lips. So it's reasonable to say Middle English speakers confused both [v] and [w].

The quoted entry goes on to say that:

The Oxford English Dictionary suggests that use of the Middle English forms with f may also have been encouraged by an association of the first element [lieu] with other English words, such as the noun leave—a lieutenant being an officer who substitutes for another who is on leave or perhaps one who has the superior officer’s leave to take command when he is absent or otherwise unable to fulfill his functions.

As for the AmE pronunciation, John Algeo in The Origins and Development of the English Language says that [lutenənt] was recommended by Noah Webster in his American Dictionary of the English Language (1828). It thus seems to be a spelling pronunciation.