Will I be able to claim if I have coins stored on an exchange? Or a Ledger hardware wallet?

Exchange deposit addresses are generally no use, as you have no way of accessing the private key. We hope that exchanges will support us and credit LTC holders with LCC automatically. No announcements yet; keep an eye on our website.

The very best way to hold coins during the fork where you know you'll have control of the keys is to use a desktop Litecoin wallet such as Litecoin Core or Jaxx.

If you use a Ledger, the simplest solution is to move funds from your Ledger to a desktop wallet, just until the fork block happens.

Part of the reason it's so great is that it's impossible for you to directly access private keys for your wallet addresses. What is possible is to use your 24-word BIP39 phrase in conjunction with an offline tool such as this one, which you must save and run locally while disconnected from the internet. That tool can derive your private keys from your 24-word phrase, however, you really shouldn't do this. For one thing, you'll need to reinitialize your Ledger wallet in order to practice safe forking. It's really simplest to transfer your LTC to a desktop wallet, and transfer it back after the fork.

IN ALL CASES: Practice safe forking. That means you must never paste private keys that hold live funds into ANY website or wallet in order to claim fork coins -- including ours. After the fork, FIRST move your LTC to a new address, THEN use the private key from the "old" address to claim your LCC.