This is one of those things that fall under the category of "Not my strongest suit"
I'm no flooring person, but I have been around contruction long enough to see what flooring pros do. I've never seen one lay a floor directly over linoleum. Every flooring person I've seen either strips the existing floor up (not the easiest choice!) or puts a new underlayment over the top of the existing linoleum. Underlament is "Luan board", a thin plywood that is cut to fit and nailed to excess with underlayment nails. When you think you have nailed it enough, nail it some more! Also take the time to be sure that the nails are set so they don't protrude and cause problems with your tiles. Special saws are used to trim the casings of doorways, where they meet the floor so the underlayment and the new flooring can slip under them. Open seams or uneven seams in the underlayment are filled in or feathered off using something like Durhams Water Putty and then sanded smooth. Offset the buttseams of your underlayment so you don't have four pieces coming toghether at a single point.
I'm assuming that your using what I call "Peel and Stick tiles. In this case, consult with your distributor or manufacturer on the use of a coating to put down on your underlayment previous to laying the tile. Sort of like a "primer" to give your tile extra adhesion.