A restaurant with a nearly quarter-of-a-century presence in Fairfield is closing its doors next month.Kim Davidson, marketing director for The Old Spaghetti Factory, told Journal-News the eaterys lease term at 6320 Gilmore Road came up for renewal and we made the difficult decision not to extend it.The restaurants last day of operations will be Sunday, May 3, Davidson said.The Old Spaghetti Factory has been honored to serve the Fairfield communi…