Most consumers will not want to do this because they don't know who they will be buying from and don't know how much they are going to spend. If they decide they want to buy from random website Z one day, making a lightning network connection between themselves and that website will be useless because establishing a lightning network connection needs to go on the regular slow block chain, so it'll take as long as a regular payment.
The only way it works is if a major exchange like Coinbase sets up lightning network agreements between other major exchanges. Then the user puts bitcoin into Coinbase and uses the Coinbase website to make lightning network payments on your behalf. This means you will probably put all your money into an exchange like Coinbase who can then run off with your money.