That depends. Some wallets like Phoenix and Breeze are backed by companies that aim for permanent channels. "Permanent" here means that EU would probably butcher ACINQ earlier than ACINQ decides to drop your Phoenix channels.

Full node setups and other LN wallets have channels opening and closing all the time. When your channel is closed, you get your money in a UTXO. But if it's not the same channel from which your funds entered LN, it's non-trivial to link this UTXO with you.