How do you determine what the 'local' currency is? Local to you or local to the client? Presumably you already know what the local currency is, so it should only be a matter of converting from the invoice currency to the local currency using the exchange rate. If you don't want this value to change as exchange rates change over time, then you will need to store it.
You may want to look at creating a plugin that ties into the Invoices.add and Invoices.edit events.
I would imagine that you could create a plugin that defines a new database table that references an invoice and defines a field for the currency (and price if you need it). Then your plugin can be used to fetch that information when viewing the invoice so that it can be displayed.
The last part, where you must fetch/display the additional information would require you to update core code to integrate it.