How to cut a ceramic toilet cistern lid?

I need to remove the lid on my toilet cistern but it's too tight to the tiles above it. Is there an easy way to score the back of the toilet cistern and break off the back so I can remove it neatly?

No!

If you are talking about about a 3 or 4mm adjustment, can you put spacers between the cistern (around where the screws go through it) and the wall ?

Any bets the tiler tiled down to the top of the cistern but not behind it.

Best way to remove the lid would be to cut the tiles above it. A small angle grinder with diamond disk.
Mark out a line with masking tape.
Cut along the top of the lid approx 1 -2 cm and then remove the pieces of tiles left.
Afterwards fill up with silicon.