Eidoo uses the standard derivation path for your LTC wallet. Because of this, you will be able to restore your LTC wallet directly with your 12 words in an external service that supports LTC.
In case you still needed to retrieve your private key, you will be able to do so via the following steps:
1. Connect to the site https://iancoleman.io/bip39/ (for more security the tool on this site can also be used in offline mode)
2. In the Mnemonic section type the 12 words in the BIP39 Mnemonic field and set the Coin field to LTC-Litecoin.
3. Check that the Derivation Path is set to BIP44.
If all the data is correct you will find the master key in the section "Account Extended Private Key".
Want to recover your ETH private key instead?