Yes and it probably already exists. The only issue I could see from building one would be who is paying the fees when channels close as that'd have to be covered in transaction fees (on the exchange) - just in case there's a forced channel closure.

Purse.io has lightning payment acceptance (the place where you can buy things from amazon with crypto at a discount) but I don't know if this is the exact way it's done there. Also lightning payments still mean the exchange is the custodian if the funds while they're there unless they're doing an atomic swap (I don't know if that would disincentivise users taking funds out of the platform if they know they can withdraw from it within a few seconds).

what he means is what the LN community call "atomic swaps"
where they trade different coins in LN

everyone knows LN can and does allow channels of different pegged currency(though they falsely pretend LN is bitcoin and only bitcoin)

everyone knows the msats in a channels payment onion is not actual bitcoin but pegged units of promise at 1:1000 rate (disclaimer: security risk:  no network audit/consensus to secure that peg rate)

but yes LN can swap coins. though with more disclaimers needed at a huge risk due to their crap code. flaws and bugs

Thanks for the replies!

I was thinking that everything can be built on the bitcoin network. If the lightning network can support derivatives then why would I need to use another chain or centralized exchange? It could use BTC as the settlement layer. Forgive me if I don't understand the lightning network fully, but it seems to me that it would be possible to do this.

I have a dream that we can exit this corrupt fiat system totally and just build everything on the bitcoin network. BTC would become the backbone of everything that happens in the economy. I mean I am struggling to fully understand the limitations of lightning, like why would I need to use any other chain if everything can effectively be done on a BTC layer 2? What are the limitations of the lightning network?

If you have some reading material on the lightning network that may help me that would be really appreciated.

Something like this already exists and it's called Kollider.
They are also working on Kollider wallet, that should work for for quick swap, send and receive coins.
On exchange you can find Synthetic Stablecoins Euro and USD that are backed by Bitcoin.
Everything is in Beta phase, so you can expect some bugs along the way, but I think this is good move forward.

Website: https://pro.kollider.xyz/
Docs: https://docs.kollider.xyz/docs/

Have you used them yet? I haven't seen your post until now. I made a topic about them earlier today after coming across them on Twitter.

[1] https://bt.irlbtc.com/view/5422825.0