Check usergroup permissions. Also, if you use the promotion system, check all groups that people could reasonably be a part of, even if they are secondary groups - because group permissions are cumulative in Xenforo.
Use the Analyze permissions tool under Groups & permissions, enter the username of someone able to do it and check the "Lock / unlock threads' permission, it'll tell you which group is allowing it. If none are allowing it, it could be an addon erroneously overriding the check for if a user can reply and is allowing it when it shouldn't be.