There might be no incentive to use Bitcoin or the Lightning Network on top of traditional payment processors. But I have to admit that fees on BTC (or the LN) are much lower than those charged by credit cards. We'll have to see what use cases the Lightning Network will bring to the mainstream world once its development is complete. The atomic swaps feature could turn out to be real useful for merchants & businesses to convert any cryptocurrency into Bitcoin or vice versa. They could quickly cash out to a stablecoin of their choice too. With instant transactions and ridiculously low fees, the Lightning Network could boost Bitcoin's adoption as we know it.
But we need to promote the benefits of Bitcoin's second-layer solution to the public. Otherwise, mainstream businesses/stores won't accept LN payments anytime soon. It's still too early to talk about this since the LN is still in its infancy. But rest assured that if it becomes successful in the long run, major retailers (like Walmart, Amazon, eBay, etc.) will begin accepting LN payments for the benefit of everyone.
I believe that merchants/businesses would save on fees by using crypto instead of traditional payments processors. It would be more cost-efficient for them to accept Bitcoin or "BTCLN" directly without going through a middleman like BitPay. The only downside is that the merchant/business would need to have a certain level of technical knowledge to send and receive crypto payments. Still, the advantages outweighs the disadvantages. If the need arises for mainstream businesses/stores to start accepting LN payments, you could expect BTC to gain traction like never before.
I'd like to see someday Walmart or even Amazon accepting LN payments directly. It would prove out to be extremely convenient for everyday people as transactions would be settled instantly at a fraction of the cost without middleman. But this could take a couple of years from now before it becomes a reality.