If it uses a blockchain, it's still an L1. At best it kicks the can down the road, and at worst, it's a scam, a distraction, and a waste. Only one blockchain is needed for all of humanity in all of the solar system for all time so long as we use distributed state that settles on L1, such as LN payment channels and RGB20 tokens.
Discussion
Based on the hash horizon of Bitcoin (~180 000 000 km or 1.2 UA) the competition for mining would remain close to the earth. So yeah, at first people living on other planets and moons will be using Bitcoin and its L2s and L3s, but those outside the hash horizon of Bitcoin will considered to not be totally financially independent as they could not mine profitably. This would be the sparkle to ignite a new planetary timechain, one sufficiently far apart from the Bitcoin timechain in order to not overlap those markets.
So long story short, there would be multiple timechains within a solar system, ones that are sufficient apart to not overlap and one with an even lower time preference (ie. longer time block).
To learn more about this, check out Bansal's article "Bitcoin Asrronomy" and/or the magnificent graphic novel of EncryptFractal "The Timechain Codex" (https://www.swanbitcoin.com/the-timechain-codex/)
Sure, but even then, layers are sufficient. Besides, if the hash horizon is within 1 AU, then that's perfectly fine for the Dyson sphere where most of it will take place, anyway.
If anything, what's nice about the hash horizon is that it protects us from extraterrestrial influence, in a way.
1 AU centered on earth, so some colonies on jupiter's moons will not be able to mine profitably.
With mining comes the virtue circle of the efficiency use/allocation of energy, so it could be a sufficient reason to launch a new planetary timechain elsewhere that is sufficiently far away to not interfere with other planetary timechain as Bitcoin.
The dyson sphere (or swarm) seems to me to be the kind of megastructure that would be constructed after the diffusion of humans on several colonies around the solar system, so it could be the type of structure associated with stellar timechain.