Is there any other name for luan that would be more commonly used in Canada? When I asked at Home Depot (I know, I know, very few options unfortunately) they looked at me like I was wearing a space suit asking for a used space shuttle.
Don’t worry so much as to the top layer of wood unless you are going to finish it as a stained wood panel. Any 1/4 inch plywood, or any thickness, as underlayment will work. If you are after a painted finished look, you need to spend the money and get birch.
HD prolly won’t have Luan at any time because the mahogany is enviromentally sensitive from some points of view. 1/4" underlayment is pretty good stuff. it should have at least on finished side and definitly no knots and doesn’t neccessarily have to be luan. Underlayment has to be solid or the voids will show up in your linoleum floors and wear out prematurely. Try a regular lumber yard instead if one is available.