Can there be any test to diagnose a suspected food allergy or intolerance?

Yes and not really: Food allergy is diagnosed by assessing the history (in the context of symptoms), and either allergy skin test or specific ige blood test. These are especially helpful in confirming a patient does not have food allergy if test is negative. Sometimes a food challenge is performed to really assess if the food allergy is present. Lactose intolerance can be diagnosed with a breath hydrogen test.