If this linoleum has a paper backing, then there's a trick to getting it off.
Basically, you remove the vinyl wear layer (and you can do that with a pry bar) and then you apply a solvent (generally lacquer thinner or toluene also works well) to a 1 foot wide swath of paper along your floor. Then, immediately cover with wax paper, and you may want to hold the edges of the wax paper down with sticks or a chain or whatever.
The purpose of the wax paper is to prevent the solvent from evaporating while it penetrates through the paper. Once the solvent penetrates down to the interface between the paper and the old glue, it will dissolve that old glue, and then removing the paper will be easy. Just scrape it off with a putty knife. Similarily, removing the old glue will be relatively easy as well. You can use the solvent/wax paper trick to soften the glue alone to make removal easier, but if you're starting to get into DIY projects, you'd do well to buy a heat gun and use it to soften the glue and scrape it off.
But, to answer your question, YES you can cover your old linoleum with plywood and then tile backer board and then tile over that. But, you don't even need to do that. If your linoleum is holding well, you can just spread a cement floor patch like Mapei Planipatch (with the Plus additive in it) over your linoleum and install your Hardiebacker panels over that.
You should be aware that the whole idea behind using a cement board, Hardiebacker or gypsum based Denshield panel before installing the tile is because these products are dimensionally stable. Wood will swell and shrink with changes in it's moisture content caused by seasonal changes in temperature and humidity, and ceramic tile simply doesn't have the elasticity needed to accomodate those dimensional changes. The idea of putting down a tile backer like Hardiebacker (preferred), Wonderboard or Denshield is to provide a dimensionally stable substrate for the tiling. There may be some cracking of the thin set in the plane between the plywood and the tile backer panels, and there may be some slow motion wiggling of the screws holding them together, but the bottom line is that all the stresses are going to be taking place in the plane between the plywood and the Hardiebacker, not in the plane between the tiles and the Hardibacker. So, the situation is very similar to living in California. There may be stresses deep in the ground below your feet, but as long as the ground your feet are on isn't moving, then you're not aware of those stresses, and neither will your grout joints, and so they won't have any reason to crack.
If your floor isn't flat enough for ceramic tiling, then there are other "bullet proof" flooring options open to you that you may not be aware of. You can, for example, install aluminum tiles, or synthetic rubber tiling. Both of these are meant for heavy duty commercial or industrial applications, but you can also use them in a home.
Check out the synthetic rubber tiling available at:
Johnsonite > Home
Synthetic rubber flooring is what you typically find in gyms because it'll stand up to the continuous pounding applied to it by exercise equipment. And, certain types of synthetic rubber flooring are used in golf shops where people will walk on it with spiked shoes, and in skating rinks where people will walk on it with skates. But, these kinds of flooring are 3/8 inch thick, whereas the stuff meant for foot traffic is only 1/8 inch thick.
