To answer this question we must understand how LN works and why the transactions are instant.

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.