Sony liquid crystal display (LCD) high-definition TVs can wear down, especially the backlight. The LCD itself does not give off light, it just changes colours, the backlight is what provides the photons necessary to provide an actual image. This backlight is just a fluorescent tube like in your lamp and it needs to be replaced periodically.
Turn off the TV by pressing the power button on the front bezel. Go to the rear of the TV and pull the power plug from the electrical socket. Wait 10 minutes for the power to drain from the LCD TV's capacitors before going to the next step.
Go to the back of the TV and locate the lamp tube replacement panel in the lower right corner. Pull the maintence cover off by hand first. Then unscrew the Phillips-head screw that secures the smaller tube door panel down. Pull the door panel off and unscrew the two retaining screws that hold the lamp tube in place. Pull the lamp out by hand and then insert the new tube. Screw the retaining screws onto either side to hold the lamp steady.
Rescrew the tube door panel back into place and then slide the maintenance cover over that. Turn the TV around. Plug the power cord into the electrical socket and turn on the TV.