Sorry to say, but if you want to do it right you will have to remove it. Otherwise moisture may get between the two layers or underneath the linoleum eventually causing it to lift. It may not bind with the linoleum, the materials may cause the linoleum to break down etc.
There are a few things to take into consideration first. What's the sub-floor?(the floor that the linoleum is glued to...is it wood or concrete?) Is the linoleum in mom's kitchen and dining room? Or just the kitchen, etc.? Because if it's in just one of the two rooms, and they are adjoining, you'll have a slight height difference which means you'll have to float one of the rooms, which you may find more difficult than simply scraping up the existing linoleum (it's really not that bad). You can tile over linoleum though, check the linoleum for tears, scrapes, etc. An accordion style gouge will cause the tile to lip, it'll change the height of that specific tile, so if you have one, cut it out completely, the void will be filled with mud (thin set). Use a Type II thinset, which is fortified. It's a little more flexible than Type I, it'll create a strong bond to the linoleum, and the grout lines won't crack. I usually take the linoleum up if it's only in one of the two adjoining rooms, so I don't have to float. It's really not that difficult to remove a linoleum floor.
