Is there a penalty for not lodging a will?

A "trustee" is someone who administers a trust. If the decedent who created the trust also created a will, it's typically just a pourover will that would never need to go through probate. If the decedent only created a will, then the administrator is an "executor." Whether that executor must file a petition for probate depends on what assets were left in the estate. There's no particular penalty for failing to do that when probate is necessary, but that failure can result in another executor being appointed to replace the one originally chosen.