i think you will have to give them pass to your litecoin account.
of course it is not good to give passwords to anybody so how it is done you move everything from your X litecoin address to a NEW one. then you give them pass to your X account, so they can verify that you owned the coins but account is empty so they cannot rob you.
something like that, it is explained on their website i think.
Uhm... Nobody will need your password for a fork except for scammers (Keyword: Blockchain...)
In general you shouldn't store any coins in exchange-wallets anyway - better use cold-wallets or a hardware-wallet.