Using the same Ledger Nano wallet app for both BTC & LTC.
Step 1: Plug in your Nano S and connect with the "Ledger Wallet Bitcoin" from Ledger.
Step 2: Choose "Legacy" to open the Litecoin wallet and "Segwit" to open the Bitcoin wallet.
Note:
You can use the same app to store the private keys for both LTC and BTC at the same time.
Make sure you use your LTC address to deposit your LTC there and BTC address to deposit BTC.