The area of floor we are having done with ceramic tile is over lenoleum which is over concrete (foundation). Do we have to take up the lenoleum? It is old but in good shape and down tight.
my guess would be yes because the tile cement won't bond to the floor. You may also want to use a cement prep on the old floor. The lenolium is also slightly flexable and you don't want that. I would rip it up but see what others say.
Programmer geek is absolutely correct. You can lay another layer of flexible flooring over flexible flooring, but not tile over flexible flooring. Not only will tile not stick directly to vinyl (although you can get around that by securing wonderboard to the concrete floor through the vinyl), but it will rot out eventually. Remove the current flooring down to the concrete before tiling.