I don't understand why you don't want them to spread. I would let them multiply at will. Give the extra away if you don't want them.

The mulch will not prevent them from multiplying. I am talking about Asiatic and Longiflorum/longiflorum-Asiatic now. Orientals don't multiply for me.

The cardboard will rot and provide improvement to your soil and your rocks will end up on the soil. Is that what you want to do? If you leave the lilies to multiply you could always move them to another spot in your garden. I don't know what will happen if you try to restrain their natural reproduction but you could always dig them after they bloom and the leaves die back and remove any new bulbils. Orientals do multiply for me but slowly in zone 7a.

Nancy