Saving costs is replaced by eliminating waste in lean manufacturing. So it is not about correcting the end result but about removing the sources for that. On the other hand lean has a broader definition about cost. Lead time to the customer, poor quality of product and non empowered employees all can be a cost in the eyes of lean.
In the effort of saving few dollars any organization should not incur more long lasting costs in other areas. For an example in the process of cutting down the cost of transportation it is important not to overlook the costs that can be created by delayed deliveries to the customers and possible loss of orders due to that. Cutting down jobs is another example. Organizations will save some money doing so. But they will loose the knowledge and the trust in long term. This can create long lasting negative impacts on the organization and will cost much more than they save today.
Higher costs are the result not the source. In lean these sources are identified with its classification of eight wastes. Eliminating these wastes from the system will automatically reduce cost for you. But if you focus just on saving some dollars you might incur heavy costs in the future.
In lean manufacturing financial documents like P&L and Balance Sheets reflects the past. To be successful in the future you need continue to find out and remove wastes from your system. In this case there is no requirement to specifically focus on cost cutting, it will be achieved automatically.