Look into Optimism and Arbitrum for current technology, or zkSync, Starknet, Polygon zkEVM for next gen L2's coming soon. There's a big list of all the current L2's and their tradeoffs at https://l2beat.com
For instance, with LN you have to be online to secure your funds, otherwise you might lose them.
L2 only inherits the security of L1 when it settles, which by definition is not that often (that's the whole point!).
The "whole point" of L2 is to reduce the amount of resources used to settle its transactions on L1. Some L2s, like Lightning Network, achieve this by settling infrequently. But other L2s, like roll-ups, achieve it by batching transactions in clever ways so that less L1 resources are used on a per-transaction basis.
It could write to L1 immediately, but your writes can still not be trusted or right.
https://www.paradigm.xyz/2021/01/almost-everything-you-need-...
I don't understand what we've gained here.