Green’s Dictionary of Slang

(US) to tell a lying story (to).

1912		R.W. Brown ‘Word-List From Western Indiana’ in DN III:viii 591: story, v. To lie, fib.
1935		J. Conroy World to Win 77: Oh, you needn’t try to story to me. I know all I need to know.
1958		E. Gilbert Vice Trap 138: Just story him [...] You went across there alone.
1986		S. King It (1987) 162: You think I’m storying you along?