Linoleum is not an adequate subfloor for ceramic tile. You need a rock solid base to prevent cracking and grout crumbling. Your best bet is to lay a 3/4" plywood subfloor right over the top of the existing linoleum. Sure, it will raise the floor, but you use a marble or oak saddle at the doorway, and you use an extension for the toliet waste, and you're good!
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