Lost(hopefully found!) litecoins

I used to have an account on BTC-e, and have a record of withdrawl from btc-e confirmation/denial link with a “purse” address. I am unsure where this purse is, is there a way to tell where these coins might be? I have the address of the coins which would be “LVxTvUaMcV52U2XAcuwax7DosriD7EdETm” Looking that address up on the blockchain it shows the amount in the email which is 7.58480000 LTC.

I am sure I downloaded and moved my coins into a wallet, but if I did would it still show on the public blockchain? I am lost as to how to find my coins. I scoured my old computer for any wallet.dat files or any sort of litecoin related files, to no avail. Is there any way to tell if I did have the coins on an exchange that got shut down? (mt.gox, btc-e)?

Thank you!!!