Jon, of course Kate1 do mean record video, whoever have heard of a 35mm film camera with a LCD screen and be able to plug into a television set?
Anyway Kate, there may be some cameras that have bigger LCD screen and able to record, but sorry I can't think of any off the top of my head, I would have to look them up, however just to let you know that even if you can't find one, I'm sure that there are accessories that can help out. There may be some kind of clip on covers for the screen that magnify the screen, there are also some kits where you can conncect the camera to devices such as iPad or laptop or similar, and use the iPad/laptop's large screen.
So you know that you can keep trying to find a camera that matches your friend's needs, but if not able to do so, just so you know there are alternative options, therefore don't give up trying if not able to find a suitable camera.