dave writes:
I already tested all over (both areas) with a toilet plunger, and the
linoleum is "stuck down GOOD'n'TIGHT" everywhere to the slab, central
areas included, wall TO wall, *NOT* just along the edges...

Just because it is "stuck down GOOD'n'TIGHT" now, doesn't mean the
lino will be so in the future.
I have heard pros suggesting nailing down the lino every 8" before
applying tile. Also, any loose or uneven areas should be
removed. Finally, make sure that the floor/subfloor underneath is
strong and stable.

Otherwise tiling over lino should go just fine, though if it were me
doing my own job, I would probably remove it as a perfectionist.