The transactions within an open channel are only stored by the two owners of the channel. The entire network does not need to store, nor does it even get to see

The transactions within an open channel are only stored by the two owners of the channel. The entire network does not need to store, nor does it even get to see these transactions. They can even be private. When the channel is closed none of the channel transactions need to be committed to the blockchain, only the final balances of the channel between the two participants. A lightning channel does require an onchain bitcoin transaction both to be opened and closed, but while open it supports unlimited transactions within the channel while it is open without increasing the onchain storage burden on the network validation nodes further beyond the two transactions to open and close the channel.