Green’s Dictionary of Slang

to burden with.

1890		Doss Chiderdoss ‘Unexpected Places’ Sporting Times 8 Mar. 1/3: His ticket soon was numbered, for our friend was promptly lumbered / On a game of nap, by someone slightly Yiddish.
1956		‘Charles Raven’ Und. Nights 116: Then three —, beg pardon, sir, three females of the species who lumbered me into my bird, got me into my present predicament, as you might say.
1961		(con. 1920s) J. Sparks Burglar to the Nobility 19: I didn’t wish to be lumbered with some mug.
1965		L. Dunne Goodbye to The Hill (1966) 142: Another bird would have lumbered me all the way.
1982		J. Sullivan ‘Ashes to Ashes’ Only Fools and Horses [TV script] Oi you, what’s the idea of lumbering me with a funeral?
1999		N. Cohn Yes We have No 185: Just a tag I got lumbered with.
2020		G. Disher Consolation 26: ‘[S]he gets hit by a bus and he gets lumbered with the kid’.