I think you would have to create an account on a different trading platform (like Bittrex)...send some LTC over there from Coinbase, trade for Etherium, then trade for Steem (LTC -> ETH -> Steem). After you hold more Steem, you could send it to your Steemit wallet.

https://steemit.com/steem/@oneyesoneno/how-to-send-steem-from-bittrex-exchanger-to-steemit-for-powerup