How can I import the Mini Private Key of a physical coin? I have a physical Litecoin based on a Casacius Bitcoin. I have the public key and see that the Litecoins are there.

Peeling back the seal/sticker revealed a Mini Private Key, but I'm having trouble importing it into Litecoin Core, importprivkey(…) gives me the error message Invalid private key encoding (code -5).

What do I need to do to import the Mini Private Key?
You must convert the mini-private-keys to regular private-key format before being able to import them in wallets such as Litecoin-core. If your keys are based on "Casascius" then you could use liteaddress.org (fork of bitaddress.org) to do the conversion. Follow these steps:  


In order to be safe download the source code from https://github.com/litecoin-project/liteaddress.org and run it on an offline and clean computer. That way you can be sure that the code you are running is actually what was shown on GitHub and running offline helps to keep your private keys safe from malwares, keyloggers,...
Run the file called bitaddress.org.html (it is not renamed to liteaddress!)
Move your mouse around (you have to, then you can ignore the result)
Click on the tab called "Wallet Details" and paste your minikey in the first box can click "View Details" button.
Depending on which address has balance (compressed or uncompressed) copy the respective private key at the bottom and import that in litecoin-core