To make transactions with Lightning Network the business that want to accept LN payments needs to create some kind of 'channel', so, let's say you have a hosting business and you are accepting Lightning Network, then you create a channel with 0.1btc. So, when a client pay to you the service of 0.002btc now your 'channel' will have 0.098 available for LN. Once the channel gets full then it broadcast a transaction in the bitcoin blockchain to confirm all the LN transactions in one real transaction on the blockchain.
Now you can see the problem with replacing VISA. The transactions are instant but the community needs those channels to spend with LN, so, my answer is a big NO. Lightning Network can't replace visa.
That's for the clarity on this. LN is mainly an off-chain bypass methodology which collects multiple payments and broadcast it to the bitcoin blockchain as a single payment.
I know LN is now officially released and we already have LN wallets available in the market. But it indeed has a long way to go before it becomes mainstream. For LN to overcome Visa, Bitcoin has to first position itself there! So even I don't see how bitcoin or LN can even stay at the same position as Visa.
It is like a newbie challenging an industry leader. Don't see it happening in our lifetime!