I think this is something to do with the older styles of lino which seemed to be more porous. I have vivid memories of my mother "polishing" the kitchen floor with a big machine with 3 big rotating brushy wheels on it...maybe this is what is needed...application of some sort of polish/sealer and then rub it in hard?
I think I might just tell DH to "bump" the tiling of our house up on the reno's list