We need something like CircControlLostBranch with which to specify which branch should be followed for actions and fees related to lost items. Since Bug 9596 the longoverdue cron can be limited by branch, but it follows CircControl when doing so. Lost item fee and processing fee refunds also follow CircControl. However, some libraries want checkout limits and periods to be governed by issuing branch but lost item behavior to be based on the owning library of the item.
I forgot about our friend RefundLostOnReturnControl, so I was a bit wrong in my first comment. The longoverdue cron follows CircControl currently. Lost item fee refunds follow RefundLostOnReturnControl.