Tile floors on a raised wood foundation?
Answers:
Take up the existing linoleum and plywood underlayment and put down those concrete board sheets as the new underlayment. It's rigid and won't flex like wood, which would make your tiles crack.
Then you'll be in great shape.
Other answers:
as long as the floor is solid (doesn't crack or squeak when you walk on it) you can go over it with a ceramic tile backerboad such as wonderboard or hardibacker and then install ceramic over that. it comes in 1/4" and 1/2" you will need to determine which to use depending on the height of the surrounding floors. It won't matter if you remove the old vinyl floor or not except for height issues.
as long as the floor is solid (doesn't crack or squeak when you walk on it) you can go over it with a ceramic tile backerboad such as wonderboard or hardibacker and then install ceramic over that. it comes in 1/4" and 1/2" you will need to determine which to use depending on the height of the surrounding floors. It won't matter if you remove the old vinyl floor or not except for height issues.