What are conflicting transactions? Does it mean BTC lost permanently? An online store recently received a payment via a wallet-to-wallet BTC payment. But after a while the total_received value went down to zero on blockchain.info. Now the address cannot be sweeped as there is no balance so the merchant assumed that the money is lost/stolen.

Tradeblock seems to have more details for this transaction:

https://tradeblock.com/bitcoin/address/1L1MSa36vaSeo8myBcGfGA3UddGDitZXai

Here's another similar one "suspected" from the same user:

https://tradeblock.com/bitcoin/address/1KsVJ1ySWVmVD5uci4mSuT98Uj65VpEzD

(icon at the rightmost column of each transaction has more details)

Can someone pls explain the anatomy of this - how to interpret and how to rectify (if at all possible).
Conflicting transactions are simply two or more transactions that spent the same UTXO in its inputs (i.e. doublespending).

The only remedy is to not treat a transaction as successful until it has a number of confirmation that satisfies you. 

It is impossible to recover from a successful doublespend attack should the conflicting transaction be included in the blockchain.