Several things could be wrong here.
Some LEDs (not ordinary bulbs) are sensitive to orientation, so if a LED is dead try removing it from the socket, rotate 180 degrees and put it back in again and see if that helps.
If you move a "dead" lamp to another,currently working socket, does it light up? If not then lamp might be bad.
Many people swap lamps with the game turned on, it's certainly doable but only recommended if you know what you are doing. Unintentionally shorting things while swapping lamps is really bad so I recommend you to turn the game off when working on it if you are new to all this.
Those green boards often have problems where a small indentation have been formed over time in the contact plane for the black plastic lamp holders. Remove one of the black lamp sockets and look at the two silver colored tracks on the board, you will probably find two grooves who causes bad electrical contact with the twist lamp holder. The easiest solution to this problem is to get a soldering iron and reflow the planes with some new solder (to remove the grooves).
It could also be an issue where the two small metal prongs on the twist socket are too flat. Try bending them a tiny bit more to make them stand out more and thus get better connection to the board.
As the other lamps seem to work it's most probably not an issue with a fuse. If you want to check the fuses in the backbox anyway then measure them for continuity outside the game with a multimeter (measuring fuses directly in the fuse holder isnt reliable as the current can go other ways and fool the instrument that the fuse is ok).
That metal lamp socket lamp can be changed either from above or below. From above you have to remove the plastics to get access. From below simply unscrew that small screw holding the socket to the playfield. Then press bulb down and rotate to get it out of the socket.
If above doesn't help then measure voltage coming to the board/lamps using a digital multimeter to see if they actually get any voltage at all. If not the problem is upstream in broken cabling, bad connectors and so on. The measuring obviously needs to be done with the game turned on so only do this if you are confident, if you short stuff while measuring you will make things much worse. If unsure then ask someone local for help.