Lengthy means going on much longer than usual. Long, with a complaint attached.
That complaint is the difference, since a long meeting is a description and a lengthy one is a judgement, and the word is nearly always faintly weary. It attaches to meetings, delays, explanations and legal processes. It describes duration far more often than physical length, where long is the natural word. Protracted is the formal equivalent and drawn-out is the informal one.
1adjectivelengthyLasting a long time, often tediously so.
“There was a lengthy discussion about the wording.”
Proto-Germanic
*langiþō
Proto-West Germanic
*langiþu
Old English
lengþ
Middle English
lengthe
English
length
English, today
lengthy
From length + -y. length comes from Middle English lengthe, from Old English lengþ, lengþu, from Proto-West Germanic langiþu, from Proto-Germanic langiþō, equivalent to long + th. Cognate with Scots lenth, lainth (“length”), stq Loangte (“length”), West Frisian lingte, langte (“length”), Dutch lengte (“length”), German Low German Längde, Längd, Längte, Längt (“length”), Danish længde (“length”), Swedish längd (“length”), Icelandic lengd (“length”).
Etymology from Wiktionary, CC BY-SA