Can you lay ceramic tile over linoleum?

If the lino or vinyl is over a slab and is well bonded, yes there are ways to do tile.

If its straight over a wood sub floor you can properly add 1/2" cement board and go over it that way.

If the vinyl is over a thin wood ( over the sub floor) you must take it up and start at the sub floor with a substrate to support tile.

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You need to lay down cement board for the tile to adhere to. The cement board is screwed to the floor at 1 screw every 8 inches. This keeps the sub-floor from moving (removes all creaking) which in turn stops the tile from breaking and the grout from cracking when walked on.

If there is nothing under the linoleum except the flooring then you can leave the linoleum in place and just layout the cement board on top of it.

If you have several layers of flooring under the linoleum you should remove all layers down to the sub-floor then apply the cement board.

Just like when you paint over a surface that has paint already. Your new paint is only as good as the layer beneath it.

Same goes for tile. The lino, will not be a good surface to use for new tile.

No. Take up the linoleum and clean the underlayment thoroughly.

simply put no,they will not adhere to the lino so will come up almost as fast as you put them down.