Yes it does seem like there's some potential for chaos on L2, for example if your channel partner broadcasts and outdated state to the main chain of fork A but your node is only monitoring fork B

I would hope that if there was a hard fork that there'd be enough lead time for lighting users and developers to get ready for it 

Indeed LN seems very fragile in that scenario

88b0c423eb

bitcoin_beginners

Sats on LN during a soft/hard fork

The fork is not based on the implementation (core/LND), a fork is based on consensus rules.

So the answer is that you should be able to close the channels on one or both forks, and you will receive whatever balance you had on the main chain of that fork.

There might be some confusion as to which fork your current LN wallet implementation is communicating with, and whether the hard fork introduces any interoperability problems with your current LN implementation.

