Yes, you can tile directly over the old linoleum, or over tile for that matter. First I will explain how to Ceramic tile over it, then how to use a regular 12 x 12 vinyl over it.
You will need to nail down metal lath. That is a product that is actually galvanized perforated ex panda metal that is used often in the dry walling. It comes 28 inches wide by about 120 long and costs about $6.
You need an air gun to nail it to the existing concrete floor, or if you have a small area a cement drill and screws will work just fine.
Once nailed or screwed down, the metal lath can then be coated with ceramic tile adhesive mortar and the floor installed much as one directly over concrete or wood plywood.
On installing 12 x 12 vinyl tile over the linoleum, that too can be done very successfully. You need to roughen up the surface with an orbital floor sander to improve adhesion and clean up the surface. An orbital floor sander can be rented at Home Depot for about $35 a day plus pads.
The vinyl tile can then be laid directly over the old linoleum in the same manner as over a regular plywood floor.