Glad it interests you :)
I'm also curious about what more knowledgeable people can say about this.

Without having the required technical background, I can't say much about implementations, but we do can make some affirmations:

• There will be no issues running a local payment system e-cash style, that's for sure. But the problem will now be at L1 level, that is, the problem will now be solely about final settlement, not the transaction itself.
• The newly added dimension to the problem is time. Bitcoin solves the byzantine general problem but without considering "large" periods of time, while in this scenario scaling will not be solely about message veracity any more. We can actually go back to the "byzantine general problem" allegory and it will be like: "ok, you can confirm the message is true, but a year later? We are invading now, the defenders might have called reinforcements or abandoned the city, or attacked the other half of the army, etc, and by knowing any of that for sure a year later will imply that going there you will find but ashes". The purism of knowing if a message is true is now being challenged by timing pragmatism. What if a full inter-planetary synchronization round end up taking decades?
• Maybe by considering a semi-isolated scheme, settlement synchronization rounds will now be defined in layers within L1. There will be an L1S settlement layer for the Solar System, and L2S settlement layers for each planet, both within the blockchain, in a similar fashion on how L1 and L2 transactions are treated now.