Yes, here’s the entry in OED for the sporting sense.
ADDITIONS SERIES 1993
Add: [III.] 11. Sport. Const. with dative of person. To give or concede (an advantage or lead) to an opponent. U.S. colloq.
1934 J. T. FARRELL Young Manhood x. 163 We’ll play fifty straight pool, and I’ll spot you ten. 1939 Sun (Baltimore) 21 June 14/2 No fighter can spot Mr. Joe Louis his entire offensive program and hope to wrest the world’s championship from him. 1972 Newsweek 31 July 42/3 After arrogantly spotting Spassky a two-game lead, Fischer had proceeded to catch up to his opponent. 1985 Los Angeles Times 14 July III. 6/2 The Dodgers,..could have spotted the Cubs an extra out for nine innings, and it wouldn’t have mattered.
One can easily see, as Oeco says, how spotting a loan could come naturally from this.