Walls and Ceilings - drywall over all vs. complete gutting...

I have to drywall a bedroom ceiling that is currently covered with those once-popular fiberous, cardboard-ish tiles. I'm assuming this means there are furring strips over plaster/lathe as well. All seem in great shape, so my question is this: can I install 1/4" or 3/8" drywall directly over all existing materials, or do I need to remove the tiles and strips, and, at the worst, also remove the plaster/lathe and go with 1/2" or 5/8" drywall?
Thanks for any help here!

I would not install drywall over the ceiling tile. My tiles were stapled to the unfinished drywall ceiling. I removed my tile and had 1000 staple holes to fill. No lathe and plaster.

Take the tile off. Now maybe you have furring strips. If they are straight make sure they are screwed securely to the joists and drywall. Maybe you have plaster. If it is straight then find the joists and screw to them. Make sure the screws are long enough. figure 1/2" lath + 1/2" Plaster + 1/2" drywall then you ought to go into the joist at least an inch. It takes a pretty hefty screw gun to put in screws that are that long. And not only that but the joists may be very hard.
On the other hand maybe the plaster is pretty good and all you need to do is spot the bad spots prime and paint.
Usually the reason someone put tile on a lid was to cover bad plaster.

Maybe the tile are adhered to the plaster. There will be a lot of gobs of glue to remove.

Let us know what you find.

Thanks, guys. I appreciate the input. I'm assuming this room is consistent with the rest of the house. It is all original plaster/lathe, so I bet that's what I'll find under these tiles. I just wasn't sure whether I could go right over the tiles and all with new, thin drywall.