can you use coin control on ledger live with litecoin?
Litecoin is a fork of Bitcoin, so according to their documentation page, yes, you can! Refer to this article:
Using Coin control. The complete explanation and how-to guide are over there. So you should be able to follow thoroughly.
does ledger live generate a new ltc address each time you want to withdraw btc and it generate new address like btc or not?
Yes, any leftover amount of coin you have sent, will go into a change address(
https://support.ledger.com/hc/en-us/articles/360033802154-Change-addresses?support=true).
should i just use electrum ltc or trust wallet for this?
Electrum LTC does also support coin control. But you should stick with Ledger Live.