is there a litecoin wallet website that does NOT store your private key serverside? blockchain.info encrypts and hashes everything clientside, as well as doing all of the signing of transactions clientside. It only sends already encrypted and signed data to the server, where the server then plugs that data into their RPC to transmit it to the network.

Does a service like this exist for Litecoin or another scrypt based alt-coin?
Not at the moment. The quickest way to set one up would probably be to work with coinpunk or fork their code and get it working for Litecoin.