Is 35rouF3Rm92Ens1ZH4bpsACzGSBLLvBygu the deposit or withdrawal address? It looks to me like the withdrawal address and that all is good. The address begins with a 3, so I assume this is a multisig wallet.
It is not possible to deposit Litecoin into a BTC wallet, so I think you have not made the mistake you believe yourself to have made. The address you have cited appears to exist on both the Litecoin and Bitcoin blockchains as evidenced here:
I am curious, from what type of wallet did you send the coins? Was it Electrum? To what type of wallet did you send the coins? Are you now feeling okay about your situation? From the block explorer output, it appear as though your 600 litecoins are safe and sound. Please advise.