Glad 'we' were able to help the 1st time 'round. Anyways,
Linoleum actually has oils and resins in it so this implies that it probably 'bleeds' through. Beings the oil is (obviously) petroleum-based, the glue on the NEW tiles may not stick anymore after a period of time. Hence, I'm going to go out on a limb and suggest you NOT put your new tiles on the old floor.
You have 2 choices: 1) Remove the old ones along with the underlayment, or 2) put a 1/4" lauan underlayment down before you install the tiles. Since it sounds like you're opting on NOT removing the existing flooring, then just encapsulate. (As an aside, I prefer to remove the old flooring because, these days, the laws regarding asbestos materials are changing, and you MAY have to disclose its existance some day if/when you go to sell the house. I know how to remove it and I know the 'issues' with it but I'm not the 'average homebuyer'. When the average home buyer hears the word asbestos, it conjures up all kinds of 'bad things'. Once their educated on it, they should be fine. Just my $.02 ...)
Of course, installing 1/4" + the tile will, undoubtedly, raise the floor that much more. I'd remove the toilet when doing this too. You may need to 'cut the bottom of your bathroom door to accommodate the new height. Perhaps others will say it's OK to put the new tiles right on top of the linoleum. (You've already read my comments.)