If your L2 has the same security and decentralization of the L1, then it's another L1. Since it has the performance part of things, it can only have either security (but then it's centralized, so it could fully securely write bullshit, which then gets written to L1), or decentralization (and then you get to write unsecure bullshit, which has no reason to either be trusted or true, and you can write that to your L1).

It could write to L1 immediately, but your writes can still not be trusted or right.