Lafayette, who had been fouled in the area for Scott Rendell to put the Cards ahead, then added a second, heading home from close range just before the hour mark.
The striker was also booked and then replaced by Giuseppe Sole after 77 minutes.
Andy Parry was substituted after just 38 minutes of Southport’s 1-0 home defeat by Gateshead.
Jim Stevenson wasn’t in action as Aldershot’s game at Altrincham was postponed.
Zane Banton netted after 10 minutes as Hemel Hempstead romped to a marvellous 6-1 win at Weston super Mare in Conference South.
Striker Lee Angol was booked as Boreham Wood were hammered 4-0 at home by Basingstoke in the same division.