How do I remove the cistern lid that has been grouted in?
Yikes. That was a really bad idea on his part.
The first thing I would try is a grout saw. It's designed to grind the grout out without damaging the tile. Hopefully grout is your only obstacle.
If the tiles immediately above the tank are insurmountable, your next job will be to try and remove them. They are partial tiles and hopefully you can remove them by sawing the grout out and prying them up (they will probably break in doing so). Once the tiles are out, hopefully that solves the problem.