Chances are this is a VINYL floor and not linoleum. But yes, the floor can not be tiled over if it's a NOT a perimeter glue down.
To tile over a vinyl floor, it must be firmly glued (all over) to the concrete and not curling at seems or edges. The floor should be stripped of wax, grease, dirt or any other build up. Roughing up is only needed if the floor still shines like the day it was new. You need to use a thinset recommended for use over vinyl or mix standard thinset with latex additive (no water).
Advantages to leaving a _well glued_ vinyl floor on concrete: Not having to strip the vinyl floor adhesive where application was excessive. The vinyl floor is one of the best anti-fracture membranes one can have on a slab floor. If you remove the vinyl floor and cracks are evident, you must use an anti-fracture membrane to stop them from transmitting through the tile.
Disadvantages: Having to listen to every Tom, Dick & Harry who tells you it won't last.
J.P.