Myetherwallet
If you are sending LTC to Myetherwallet just the same as you commit suicide. wkwkwkkw
look here :
https://coinmarketcap.com/currencies/litecoin/#markets
you can put it in various markets.
but if you want you can keep it in LTC offline wallet
You will loss your litecoin if you send it to myetherwallet because its not altcoin wallet mate.
I think store all of your altcoin in the best exchanger is best idea so far. Because if not, you need many wallet as many as your altcoin.