Had the same problem with the same type of latch on my 2013 Micro-Lite 23LB. There's a link to a thread on this forum about it ...click HERE
The latch photos don't show on that thread, but they can be seen on one of my picture albums of mods I've done on my Micro Lite which includes photos of a broken (and a new in a bag) screen door latch like the one shown on your photo. Click HERE
to see them.
There's also another, later thread concerning the same broken latch issue HERE
Just last week I removed the repaired latch and replaced it with one that's usually used on Colman (or other) popups. It was the only latch I could find that had a low enough profile to fit between the screen door and the outside door. I also had to modify some of the inner workings of the latch to make it work. That made the lock mechanism inoperable, but I always lock the outside door when away from the RV. I also installed a magnet to keep the screen door attached to the outside door when open for loading/unloading the RV.
It took a couple days of thinking, fabricating and drilling (including a 7/8" hole), but finally got it installed. Thought I'd end up screwing up the whole screen door frame, but somehow it all worked. I still have a few spots I have to touch-up with some black paint.
Here's a link to a similar latch like I installed: JR Products 11675 Black Locking Camper Door Latch
And here are some photos of the new latch on my Micro-Lite (not great pics...took them tonight with flash):