I think you may have one that originally had the chain for the lift. I've only seen them with a chain or a cable, and the grove is wide like the chain type have.
Pretty neat the fixes put on it to make it work. Normally they have a long screw that goes into a hole on the narrow end of the flap, through the end of the chain/cable in the grove and into the other side of the table.
I agree about worrying about a leather strap holding it up. there is quite a bit of stress on it when open, and it's constant as there is nothing but the tension of the flap open that holds the machine up. I'd be more worried the ends are going to rip out than anything else.