Yes, you r right! Lightning is a decentralized network using smart contract functionality in the blockchain to enable instant payments across a network of participants. Their slogan is Transactions for the future
So why lighting transactions are fee-free?
Assuming merchants eat the transaction fee as they do for credit card fees, it will save merchants a lot of money (>2%). Note however that for large Bitcoin purchases just doing a standard blockchain transaction will be cheaper than using the LN. Even with current transaction fees, if you pay $1000 for something with Bitcoin with a $5 fee, if LN has a 0.5% fee then it'd also be a $5 LN fee, so using those hypothetical numbers that would be the break even point where $1000 use normal bitcoin transaction. LN is meant for many small purchases and will be much cheaper than Bitcoin when you use it for many small everyday purchases.