If what you want is a more technical answer of how the balances in a LN channel is trustlessly updated, then you should probably read a more in-depth resource, it's a complicated topic. But I'll try to give you some idea.
Every transaction in a LN channel is not a simple transaction, it's a smart contract transaction that, if broadcasted, closes the channel automatically but have multiple ways of spending it further, and one of those ways allows a party to get all the funds if he has proof that the counter party cheated (closed the channel using and old-state transaction).
So those transactions that are created are never published if both party cooperate, instead, they serve as a forced-closing mechanism if the other party is uncooperative
That was just a high level view of updating channels, but opening a channel and routing a payment is another story
Every transaction in a LN channel is not a simple transaction, it's a smart contract transaction that, if broadcasted, closes the channel automatically but have multiple ways of spending it further, and one of those ways allows a party to get all the funds if he has proof that the counter party cheated (closed the channel using and old-state transaction).
So those transactions that are created are never published if both party cooperate, instead, they serve as a forced-closing mechanism if the other party is uncooperative
That was just a high level view of updating channels, but opening a channel and routing a payment is another story