This is a european style lock where you turn the handle up for the strike to come out and then turn the little knob underneath to lock it. Can a DIYer convert this lock into the type where a key is needed from either side.
Maybe I'm missing something others have seen, but to me that looks like a standard euro lock barrel.
Look at the face plate of the lock and see if it has this extra screw.
If so, that's all that holds the barrel in. All you need is a replacement double euro of the correct length. You just remove that screw, then waggle the key in the lock [or thumb turn in this case] & pull it towards you.
The entire interlock mechanism of the door itself is managed by the handle, not the lock. All the lock does is prevent the rest of the mechanism from moving.
Note that the barrel really shouldn't ever stick out as far as that picture, most especially on the outside; it makes them easier to break into. Get one that is flush to the outside & also is marked anti -bump, -pick, -drill, -snap.