A Lightning Network transaction results in one of two things - a proof that a certain amount of bitcoins can be withdrawn at any time (minus some delay), or a proof of cheating. Surely a proof that you can withdraw a certain amount of bitcoins is more-or-less equivalent to that many bitcoins, and therefore any rational actor - including your suppliers - should accept it as such?
This isn't equivalent to unconfirmed transactions - it's tokens of exchange which directly and provably represent bitcoins. Settling on the blockchain shouldn't even have to happen monthly.
One of the other interesting things is that Lightning Network allows for payment in one cryptocurrency while you hold another by channeling it through a very simple, provable currency exchange. This could behave similarly to, for example, paying for something in USD when you hold GBP - practically automatically. So the lack of scalability in Bitcoin's blockchain might not matter so much - if something else turns up that's better for a given person holding money, they can start using it while still continuing to trade with all the people using Bitcoin.
IMHO, cross-chain transactions like this are one of the most important parts of Lightning Network - suddenly, network effects around a specific currency don't matter so much, people can hold whatever they like - Bitcoin people can trade with Litecoin people who can trade with Ethereum scripts, and when something new that solves more problems turns up, people holding that can still buy VPSes with bitcoin.