attach an IKEA Lillangen cabinet to the wall above tiles
You can use the supplied mounting system if you put a spacer behind the bar that mounts to the wall. ( between the bar and the wall to bring the bar out to the same plane as the tile.) 

The spacer will need to be the correct thickness, 

I.E. measure how far off the wall the tile sits.

If you do not have a planer or table saw  You may need to sandwich a couple of things to achieve your thickness.

You need to make sure you secure the bar into structure (studs).

You could use double sided tape on the bottom corners to keep it against the tile.