Not being familiar with what is used where your at, but I am going to bet that the linoleum is going to need to come up along with its subfloor.
New subfloor put down, then new flooring. Another option is new subfloor on top of that now, then new flooring on the new subfloor.
That glue is going to be hard to get up. Almost always it involves nasty Chemicals, heat and lots of being on hands and knees, aching back, putty knives getting glue that won't come off consistently and it needs cleaning.
Just way easier to do the other 2 ways. And faster.