lets word it a different way,
exchanges accept bitcoin but while an exchange holds the bitcoin, they separately allow users to play with their 'balances'(mysql database) to make orders.
exchanges are not bitcoin, they are a SERVICE/BUSINESS layer at the edges of bitcoin, but it is not bitcoin.
the trades do no appear on the blockchain. the trades are incompatible with bitcoin consensus
only the deposits and withdrawals are part of bitcoin. not the service offering itself.
LN is just a service layer.
even blockstream admit LN is a second layer.
even blockstream admit LN is OFFCHAIN.
This is a false analogy. While you do not own the Bitcoins on a exchange, which is a service, you very much own the coins locked within a payment channel (with or without LN). *Nobody* can take these away from you, which is not the case with exchanges.