When installed above a wood floor the stone or tile generally requires grout with a flexible additive in order to survive the movement that takes place as the floor responds to the many and various stresses it is subjected to through it's lifetime. That is why most floors of this type are not laid without grout lines. Since your cabinets are already in place, building up a thick enough bed under the tile or stone to prevent this flexing may leave you with too low of a toe kick under the cabinets after you apply the finished surface. It appears to my eye, from the photo, that you have vinyl and not true linoleum. I can easily be wrong about this and do not mean to offend in any way. It is all good, there many ways to skin a cat, but the toe kick is important. and is many times left out of the calculation. it was because you expressed the desire to do without visible grout lines that I suggested the linoleum. It is a different material than vinyl, and can both look good and wear well. humbly, elrey