It used to be very common to put tile up on whatever the wall was and seal the the tile.
Tile over plaster walls.
I have repaired tile jobs that were over 20 years old that the tile was applied directly to regular sheetrock and plaster walls.
If plaster is any way compromised you should tear out to studs and start over.
Can you lay tile on plaster walls.
You would have to remove the plaster and replace it not with drywall run from a contractor who says that.
Mold does not grow on cement.
Loose paint must be scraped.
But with cement board.
However tiling over tile can add quite a bit of thickness so make sure your wall can handle the weight.
Not all plaster wall surfaces will support the tile properly.
Scrub the wall tiles with diluted degreasing cleaner and a nylon scrub brush.
Mix degreasing cleaner with water in a bucket using a dilution recommended by the cleaner manufacturer.
Adhesive grout and tile 20kg max weight onto plaster.
Don t use paint glue pva wall paper paste only use the primer recommended by the adhesive manufacturer of your chosen tile adhesive.
Cover with cement board tape off.
Or flatten walls with a latex modified skim coat product.
Testing the wall for durability.
The problem otherwise is that grout is porous and any slight crack will cause moisture and mold on any other surface.
Layer newspaper on the floor across the bottom of the tiled wall.
You should not tile over wallpaper glossy surfaces lead paint or plywood.
Follow manufacturer instructions to a tee.
Then rinse the wall with a water dampened.
You may tile over existing tile painted or unpainted drywall plaster and textured walls.
That is true you cannot tile over plaster if that s your plan.
This was back in the 80 s.
Bring plumbing to code.
If you re not sure if you have lead paint test kits are available.