DIY said:
.... sealer in it when mixed .... Can a type of thin set ... linleum tiles?
If it's a shower, you still need a waterproof membrane underneath. Sealer is never pre-mixed in any cement product, AFAIK. Because it is a pore filler that closes up some of the spaces between grains of sand, at and near the surface. Pores = spaces. If your goal is to get good looking grout that never needs sealing or resealing,
buy epoxy grout, not portland cement based grout. Price is no object when you want the best look after all that planning and execution up to this very last step, i.m.h.o.
Linoleum is a good substrate for many thinsets; this is confirmable by consulting the thinset manufacturers' themselves, e.g. by reading the writing on the thinset package, or by calling the 1-800-tech-support hotline number that is printed on the package, or by reading the thinset manufacturer's web site. How clean is clean, is a question that is never easy to answer in words; to be sure you really don't have any nuisance chemicals on the surface of the linoleum, why not abrade the surface with sandpaper or steel wool? It'll destroy the look of the linoleum as a surface wear layer, and that is OK. In fact it'll be better than OK, since it roughens up the surface, and all roughness is always good for thinset sand grains to get lodged into and for thinset glue to stick to.
Of course the linoleum may hide problems underneath so the fact that it is linoleum on the top layer is not a guarantee that your tile will never crack. It's still your responsibility to check whether floor joists and plywood are strong enough, etc. Tile needs a non-flexing floor. Linoleum is a padding membrane. Just like cork which is used worldwide as a padding membrane under tile. Padding = soundproofing, heat insulation, mechanical decoupling. Linoleum has cork in it as one of its main ingredients.
david