I'm not all that familiar with products like Trezor but from what I've read, there's no way to get the private key out if it so you wouldn't be able to do it. Don't think I'd like that myself but I guess that's the price one has to pay for having the additional security. However, if you had a separate wallet and then imported the private keys into Trezor, and you can still get or have that private key, you should be able to do it. You might want to ask the question on their reddit though.

https://www.reddit.com/r/TREZOR/

Edit: I just found the following info but it applies to bitcoin. Might be able to do the same thing with litecoin if you can find a wallet that uses a passphrase as well. There's this one https://electrum-ltc.org/ but it talks about a 12 word phrase and Trezor uses 24 so not sure if you can make it work or not.

Remember, once you get your private key, but before you import them into the LCC wallet, you want to move all your coins from your Trezor wallet to a brand new one so the old one has 0 in it.

"If you want to see the private keys you can create a wallet on Electrum using the seed words from your Trezor. This will create the bitcoin wallets for you where you will be able to see the private keys. I will however strongly advise you not to do this. If you do this you might compromise the 24 seed words and this is the last thing you want to do. Those 24 seed words is like a master private key. Anybody who gets their hands on them have full access to your whole wallet so consider them as compromised if they have 'touched' a computer."