(This is dependent on the number of transactions made,
make a single transaction on LN and you paid more than a single onchain bitcoin transaction.
You have to make multiple transactions to the exact same person to save the most on fees.)
You are confused between direct payment channels and the actual Lightning
Network. Having such a network is the whole point of solving the direct payment channels issue you pointed out. You can learn more about the Lightning Network
here.
To answer the question : using the Lightning network is viable if you expect to do more than 2 payments using it. You will in practice have to pay some additional on-chain transactions to reload your channels.