Is it OK to install a 3rd layer of linolium on top of the 2 old ones?

They do make floor adhesive to glue down more than one floor, as long as the floor underneath isn't damaged or loose its OK to do , but only if you get the right glue.

I preferr to get 1/4 ply installed then lay the floor but its up to you, you may not have the room to build up the floor