There are a multitude of devices intended for illuminating a book or kindle, that are a battery and switch with a built in clamp, a flexible neck and a white LED. One of these should fit your laptop lid
That's if you don't fancy buying, or making, an "led on one end of a flexible metal arm, and a USB plug on the other"
In terms of stuff you already have, perhaps use some string to make a necklace, tuck it behind your phone in its protective case (or even just tie it like a gift wrap so it holds your phone) then sling your phone round your neck with the torch activated. You could keep it plugged in to remain charged. If you have a desk stand you could put your phone in that. If you don't have a desk stand, you could make one (shape one out of modeling clay, cut a slot into a potato etc then wrap it in sarin wrap so it doesn't contaminate the phone) or repurpose a phone holder intended for a car (one that clips your phone to the AC vents) so it holds your phone at the top of the screen, looking down onto the keys