Nese? ba "hung" and "hanged" habban same andgiet under þæt cynn, swa swa "tucienne mid grin". On teoþa ældu Englisch, 'hang' wesenne fram wordum hangian (to hang, to gældan on, "Ish hangode on þec") ond hon (to hang, to suspendit, "Ish heng heora on cros") in geong Englisch, ba þa strang word (hang -> hung) ond wac word (hang -> hangd) beoþ riht under þæt cynn, sīþþan we forēode mæst of usser eald gebiegednessa gesteal.
No? both "hung" and "hanged" can have the same meaning of "to lynch". In tenth century English, 'hang' came from two words: hangian (to hang, to depend on, "I hangode on you"), and hon (to hang, to suspend, "I heng them on the cross"). In modern English, both the strong verb (hang -> hung) and weak verb (hang -> hangd) are valid versions of the same word, since we largely forgo our old word inflection system.
Hon and ahon was the OE word for execution via supendion, and it was a strong verb, so when it came into Middle English (a mix of Old English and French), it became one word, "hangen", with both "heng" and "hanged" as its past tense. Now, when we invent new word, they are only really weak verbs. But since this comes from Old English, people still use both as a holdover.
Also, just because legalese and formal legal speak is fussy when it comes to using "hanged" and "hung", doesn't mean normal people don't just use both. there is no special meaning in the '-ed' version, it's just the weak verb formation. It's like saying that "knew" and "knowed" can't be used interchangeably, just because "knowed" is proscribed in legal contexts. It's just a special voice, where some speakers more commonly use "handed" to mean "suspend by noose".