Wall preparation is an important step when you in install tile on a painted wall.
How to install tile on plaster walls.
Plaster walls became popular due to the durability and strength of the surface and are more common in historic homes that drywall.
Some preparation and a certain style of installation makes the process easier and more successful.
You may tile over existing tile painted or unpainted drywall plaster and textured walls.
If you re not sure if you have lead paint test kits are available.
Oil based paints can create a problem with tile installation consider removing this paint with paint remover or via sanding the paint away prior to installing the tile.
However tiling over tile can add quite a bit of thickness so make sure your wall can handle the weight.