Hi and welcome.
It looks like a bog standard mortice lock.
Take the handle off. That ring, or the one on the other side might pull back or unscrew and reveal some screws through a plate that secures it to the door. Remove the usually square shaped rod.
Take the two screws out that secure the lock to the door and pull it out. You can take that to a DIY shop and match it up to one to replace it.
You can re-use the original handles.