Now, in the Lightning Network, all transactions are stored by all parties that have some open channel between them. There is a need for watchtowers, sometimes some payments are impossible to route because of too low amounts on "proxy peers". How it will turn out if we put all of this stuff on a sidechain? On Bitcoin, there still will be two transactions: one depositing coins into the sidechain and another, withdrawing them. Both can be constructed in the same way as in LN.

Currently, in the Lightning Network, nodes have to be online 24/7, all the time, because in other case someone could send some older transaction and close the channel with older account balances that it should be closed. If they cannot be online, they have to use watchtowers. In the sidechain, there will be no need for using additional watchtower, because every sidechain node will act as a global watchtower for the whole network, as it is organized in Bitcoin when you can send on-chain transaction and wait for confirmations.

The routing problem will be solved by creating different closing transaction. If Alice and Bob have some channel, but Alice wants to send coins to Charlie, which for example uses only on-chain Bitcoin coins, then all that is needed is creating a bit different closing transaction, taking Alice and Bob coins as an input and at least three outputs that could be spent only by Alice, only by Bob and only by Charlie.