I doubt the bottom layer is old lino, it has no pattern to it.
It does have a bit of dark swirl to it, not entirely featureless. If it's flexible that's the only thing that makes sense. 2mm is too thin to be fibre cement sheet.
IMHO the top layer plus chipboard is low risk if they just stapled it to the existing floor. The layer on the floor would depend on how well glued it was. If it lifts up like the photo I'd do it. The last time I asked at the Wgtn landfill householders could dispose of 20kg of asbestos waste without charge.