In general when child case tries to update the data to Parent it first acquires lock and once it's acquired then it will update else it throws error.
Following solutions might work:
Solution-1. If Optimistic locking is suffice for your requirement it can be done at parent level which subsequently propagates config to child cases then try updating date from child to parent. If some one locks the case when he submits his data an info message like already updates are made please refresh kind of message will be displayed.
Solution-2. With default locking only, you can check whether parent case lock exists with current user or not if not then queue for standard agent so that it can update. In standard agent check parent case is locked by any one or not, if no one holds then child case data can be updated else re-queue.