Green’s Dictionary of Slang

(US) to sit down, to lie down.

1839		C.M. Kirkland New Home ii 17: Jist come in, and take off your things, and lop down, if you’re a mind to, while we’re a getting supper [DA].
1892		F.P. Humphrey New England Cactus 34: You’d best lop down to the lounge and get a nap [DA].
1901		Monroe & Northup ‘College Words and Phrases’ in DN II:iii 143: lop, v. ‘To lop oneself down,’ i.e., to recline comfortably.