When I try to take a picture the camera asks to be turned off

Your lens mech is jammed

PSP Tech

Unfortunately, this error means nothing - or rather means "there is something wrong with the camera" - which is not very helpful.

The camera runs a bunch of tests when it starts up, if any of these fail then you get the "turn of and off" message.

Most common reason for this error is a problem with lens mechanism/autofocus etc. The lens in LZ2 (and most compact zoom cameras) is easily affected by dirt getting in through gaps between zoom barrels (a grain of sand is a killer).Usually to fix this you need to completely strip the lens mechanism which is a rather fiddly operation.
If you are lucky it's possible that it's just one of the camera functions that is malfunctioning. Try to power on the camera on each mode to see if it makes any difference. Try to switch off the flash - I've seen it on 2 occassions that flash circuit failures caused the "turn off and on" message. Try to do a "reset to factory settings" from the menu.
Good luck,
Raf