c.1300, "a bed," also "bed-like vehicle carried on men's shoulders" (early 14c.), from Anglo-French litere "portable bed," Old French litiere "litter, stretcher, bier; straw, bedding," from Medieval Latin lectaria "litter" (altered in French by influence of lit "bed"), from Latin lectus "bed, couch," from PIE *legh-to-, from root *legh- "to lie" (see lie (v.2)).
Meaning extended early 15c. to "straw used for bedding" (early 14c. in Anglo-French) and late 15c. to "offspring of an animal at one birth" (in one bed); sense of "scattered oddments, disorderly debris" is first attested 1730, probably from Middle English verb literen "provide with bedding" (late 14c.), with notion of strewing straw. Litter by 19c. had come to mean both the straw bedding and the animal waste in it after use.