Level2 and Lightning is not well defined. If you move money to a third party, even if it is within the constrained of a locked contract, then I don't think that will solve the issues. Blockchain does not know about offchain and moving between offchain and onchain requires liquidity and a pricing mechanism. That is exactly the problem with side-chains. If you have off-chain transactions on an exchange, they are ID'ed in their system, subject to KYC/AML.