The linoleum should have a 1/4" underlayment stapled into the old subfloor. You can try to scrape the old linoleum up (not a good choice)...or simply pull up the old underlayment and linoleum together. That should bring you to a nice level subfloor. I'm not sure you'll have to lay a new 1/2" subfloor, but either way you'll definitely have to put down new 1/4" underlayment in prep for the new linoleum.
I just went through the same process in a master bathroom/dressing area. It took me about an hour to scrape up 1 square foot of the old linoleum (trying to save the underlayment) and about 3 minutes to rip up the underlayment and linoleum together. A flat bar and elbow grease is all it took.