Yes. Lactose intolerance refers to the inability to digest the sugar lactose in milk. This has nothing to do with ige antibody to milk proteins.
Yes. Lactose intolerance is due to the lack of lactase in the GI tract. This is te enzyme tht digests lactose. Without it a person gets gas, cramping and diarrhea despite not having any allergy. Bacteria in the colon cause the gas and the sugar (lactose) acts as a laxative.