Is your lino cushion backed?

Is it over luan?

Is it a cheap builders grade that can shrink over time?

Is it totally glued to the floor?

Is the subfloor under it capable of supporting a ceramic tile installation?

What is the size and spacing of your floor joists?

What is the unsupported span?

If over a cement slab, are there any cracks in the slab indicating movement/settling?

Theres a lot to consider. Remove the doubt and remove the lino and luan first, then build up the floor to where it needs to be for ceramic.