Getting Litecoin cash out of my Trezor I am trying to get my private key out of my Trezor in order to access my Litecoin cash. 
I used the following site in order to generate the private key out of my 24-word recovery phrase: https://coinomi.com/recovery-phrase-tool.html

Many addresses get generated out of it. When using any of these keys into the LitecoinCash core wallet (ie. import private key), I am being asked for my passphrase (supposedly word 25th if ever set up, which I did not) and cannot access my Litecoins. I guess I am not generating the correct private key!?

Any advice on how to extract these Litecoin cash out of it?

Cheers
LCC-core is not asking for your Trezor passphrase (25-word) which, as you said, you didn't set up.  LCC-core is asking for your wallet.dat passphrase which is the passphrase used to encrypt the contents of the LCC-core wallet.dat file.  This was a passphrase you set when you originally installed and set up the LCC-core software.

Just a point of advice.  You might be better served using the Electrum-LCC software since it can talk directly to Trezor.  No need to extract private keys (which is inherently risky)