I'd picture Lightning more like an account shared by two parties where deposits and withdrawals are costly but how you split what's in the account is up to the two parties involved, and nobody else needs to know about anything but the final balance.

Lightning then provides tools to manage trust issues and to let you bridge between multiple such shared accounts, forming a network.

So Lightning reduces the number of transactions that are visible on the blockchain. What I've described should be simpler and largely orthogonal: it would allow growing the amount of information covered by a block, without increasing the block size. That information does of course still have to be somewhere, so this wouldn't result in a reduction of the number of transactions nodes have to deal with, similar to directly increasing the block size, but avoiding to have to move one huge chunk of data around at the time of accepting transactions into the blockchain, since that data would already be in the mempool.

- Werner