Do leaves leave?
Solution 1:
According to the Oxford Dictionary Online, leave (as in 'to leave') comes from:
Old English lǣfan ‘bequeath’, also ‘allow to remain, leave in place’ of Germanic origin; related to German bleiben ‘remain’.
And the other one is from:
Old English lēaf, of Germanic origin; related to Dutch loof and German Laub.
Even so, 'leave' as in tree isn't spelt like that - it's leaf for singular and leaves for plural. Just another irregular English plural!
Solution 2:
Many words in English that end with the letter "f" have either an optional or required plural form that changes the suffix to "ves." This doesn't imply etymological roots shared with homophones that likewise end in "ves."
Consider these numerous examples:
calf - calves
half - halves
knife - knives
leaf - leaves
loaf - loaves
life - lives
wife - wives
shelf - shelves
thief - thieves
yourself - yourselves
Some words can have both endings ves or s:
scarf - scarfs/scarves
dwarf - dwarfs / dwarves
wharf - wharfs / wharves
handkerchief - handkerchiefs / handkerchieves
Oxford English Dictionary describes this phenomenon under "Form History" for leaf:
In Old English as a strong neuter the word is typically unchanged in the nominative and accusative plural (in Northumbrian also with vocalic ending); unchanged plurals are sometimes still attested in early Middle English, but are quickly supplanted by the -s plural. The stem-final inherited voiced fricative was devoiced word-finally in Old English, but voicing was preserved before the vowel of the inflectional endings (although the consonant is written f in both positions). The resulting variation in the paradigm is continued in modern standard English in the distinction between the stem forms of the singular and plural (forms in regional varieties show analogical levelling in both directions).
However, this derivation of the plural form generally has no relationship with homophonic words. In the case of "leave" as in "to depart," OED offers a distinct derivative chain.
Leave:
Origin: A word inherited from Germanic.
Etymology: Cognate with Old Frisian lēva, Old Saxon lēvian (Middle Low German lēven), Old High German leiben (Middle High German, early modern German leiben), Old Icelandic leifa, Old Swedish leva (Swedish regional leva), Gothic -laibjan (in bilaibjan : see beleave v.) < an ablaut variant (o -grade) of the same Germanic base as live v.1 and belive v.1
A similar comparison can be made with the related words "live (verb)" and "lives" as plural of "life," which have an etymological relationship, albeit a distant one.
Live (verb):
Origin: A word inherited from Germanic.
Etymology: Cognate with Old Frisian libba (West Frisian libbia), Old Dutch libben (Middle Dutch lēven, Dutch leven), Old Saxon libbian, libban (Middle Low German lēven), Old High German lebēn (Middle High German leben, German leben), all showing a similar semantic range, Old Icelandic lifa to live, to remain, Norn (Shetland) liva, lava to live, Old Swedish liva, leva, (runic) lifa to live (Swedish leva, †lefva to live; the sense ‘to remain’ is expressed by the prefixed verb kvarleva, †qvarlefva), Old Danish livæ, levæ to live (Danish leve), Gothic liban to live < an ablaut variant (zero grade) of the same Indo-European base as belive v.1 and leave v.1 Compare life n.
Life:
Cognate with Old Frisian līf life, body, person, Old Saxon līf life, body (Middle Low German līf, lief life, body), Old Dutch līf life (Middle Dutch lijf life, body, person, Dutch lijf body), Old High German līb life, body, way of life (Middle High German līp, līb life, body, German Leib body), Old Icelandic líf life, body, Old Swedish lif life, body (Swedish liv life, body), Danish liv life, body < an ablaut variant (e-grade) of the Germanic base of live v.1 (zero grade) and leave v.1 (o-grade).
Leaf, on the other hand, stands apart completely from "leave," "live," or "life."
Leaf:
Origin: A word inherited from Germanic.
Etymology: Cognate with Old Frisian lāf leaf, foliage, Old Dutch louf leaf (Middle Dutch loof leaf, foliage, Dutch loof foliage, also (now regional: southern) leaf), Old Saxon lōf foliage (Middle Low German lōf foliage), Old High German loub leaf, foliage (Middle High German loup leaf, foliage, German Laub foliage), Old Icelandic lauf leaf, foliage, Old Swedish löf leaf (Swedish löv leaf, foliage), Old Danish løff (Danish løv foliage), Gothic laufs leaf, lauf foliage, further etymology uncertain, perhaps < the same Indo-European base as Old Russian lupiti (Russian lupit′) to peel, strip off, undress, rob, Polish łupić to peel, strip off, rob, Serbian and Croatian lupiti to peel, strip off, strike, knock, Lithuanian lupti to peel, skin, laupyti to tear off, and perhaps further related to the Indo-European base of Early Irish luib plant, Old English lybb (medicinal) drug, poison, charm (see lib n.1) and perhaps also classical Latin liber inner bark of a tree, bast, book (see library n.1).