I just implemented a latch on a camper top I'm making for my Jeep-tub trailer, here's what I used. This one has a knob on the inside, which you wouldn't need. (Ignore the hinges). Lots of these are on ebay, here's one without the inside knob that should work for your application:
https://www.ebay.com/itm/Toolbox-Lo...938109?hash=item41c2ac2dfd:g:8VwAAOSw5UZY94b8
Installed:
It's a slam latch, which means you can slam the door and it will latch, no need to hold the latch open while closing. To facilitate the slam action and provide a striker to hold the door snug against the door jamb, I used a striker plate from an ordinary household door. I don't have a photo of that handy but will take one if you think this is a way you might want to go.
BTW can't tell if there's any flex in your door, but if there might be then you might want to put two latches in, one towards the top and one towards the bottom. Or reinforce the door with a rib on the inside to prevent flex.