Not a super academic source, and it doesn't give a definitive answer, but you may be interested in Christopher Beam's 2009 Slate.com piece "When Did Drunks Start Wearing Lampshades?: A history of tipsy tomfoolery", which has some early uses of the trope. The earliest use he mentions where it's associated with alcohol-driven debauchery is from a 1928 piece in the Baltimore Evening Sun

#Life of the Party

[...]

It is usually customary for the life of the party about the middle of the evening to put a lampshade on his head and give an impersonation of [Scottish soprano] Mary Garden, after which he tells a joke that is not meant for mixed company.

[...]

But he leaves the host and hostess wondering whether the success is wroth the damage done to the lampshade, which will never looks the same.

He also points to Paul Harrison's column "Hollywood sees odd households" (Google archive) which writes:

[...] although [John] Barrymore would be quite a trial to any orderly housekeeper because at any moment he's likely to drag down a lace curtain, clap a lampshade on his head and play a scene from Shakespeare.

Beam speculates that this originated in vaudeville and was popularized in silent comedies, pointing to a use where Chaplin wears a lampshade to disguise himself, but this is not really the same sort of debauchery-filled trope.

There's also some discussion on tvtropes.org: Lampshade Wearing, which provides some examples of the trope in popular media.