Therefore, I decided (after reading info on the Net) that I can place
my ceramic tile on top.

Just pull up the linoleum and put down a real subfloor. Tile is a lot
stiffer than you'd think. If you don't lay it down on a VERY stable surface
it'll just crack. Either on the grout lines or within a tile. Why bother
to go through the effort of laying decent tile only to have it get ruined?