Your sister absolutely needs to take action, but she should tread very lightly here. Because this was another church, she probably has no way of knowing for sure how the auction was organized. The donor might not be the only person who knew the exact terms of the item. Someone else may have stolen it. Someone may have been worried that the dinner would go to waste (that would explain the repeated calls to see if anyone had picked it up yet) and decided to claim it, either for themselves or a family in need. Obviously, it would be better to call the winner, but who knows whether or not they had that information? Basically, there are a number of possible explanations for what happened.
Your sister should call the church, yes, but she should not make a direct accusation unless she is 100% sure that it was the Turkey lady who did this. (Say, the deli manager shows her a signed receipt with Turkey Lady's signature.) Your sister should stick to the facts. When she gets in touch with the person in charge, she can say something like: "I bid on and won the turkey dinner from X deli at the charity auction last week. When I called to claim it, the deli manager seemed to be confused about it. I faxed him the coupon and he called back, telling me that somebody else had already claimed it. Apparently, another woman had been calling to see if it had been picked up. I'm not sure if there has been some sort of misunderstanding. Was there more than one turkey dinner available and the deli had a mix-up?" In short, your sister should try to figure out what happened before suggesting one solution. It would not be appropriate to ask that the donor reimburse her if it turns out that one of the organizers (or someone else who bid on the dinner) was at fault for stealing it.