My thoughts on how future Martian colonizers could use BTC.
Martians won't be able to mine BTC assuming that speed of light radio communication is the maximum transmission speed available at the time. Read Bitcoin Astronomy to learn about the law of hash horizons.
However, Martians are not blocked from broadcasting on chain transactions and verifying blocks with their own node. They will just experience a significant delay that could have unexpected usability bugs. For example, suppose a corporation has a multisig address and both the Earth and Mars headquarters have keys to spend from it. If the earth HQ broadcasts a TX, it's likely to confirm in 10 mins, however, the martian will not see that anything has been spent from the multisig until 30+ mins later. The Martians will forever be (on average) three blocks behind the main chain.
If the martian HQ attempts to spend from the shared multisig soon after the earthling HQ broadcasts, the martian transaction may be purged from the mempools since it's attempting to spend a UTXO that has already been spent.
In the context of LN channels, a martian should be able to open and close a channel cooperatively (with expected delay) since these actions are just on chain transactions.
However, the martian LN node will start to experience some issues when trying to pay an LN invoice from an earth node.
LN nodes are quite chatty. Each node builds its own model of the network topography by gossiping to all it's peers about the new nodes, channels, TLD (time lock delta) policy updates, and fee policy updates.
So the martian node will have a local network graph that is (on average) 30+ mins out of date for all earth nodes. If the martian attempts to craft an onion for a route using a channel that doesn't exist, or by supplying the wrong fee for a channel, the payment will fail.
That assumes, that the node is even able to craft the onion in the first place. This part might take a while because construction of the onion requires a lot of back and forth communication to generate and exchange shared secrets to do all the encrypting, verification, and byte padding of all the layers of the onion. If we assume a 30 minute delay, construction of an onion with just 3 hops, might take hours. Furthermore, they'd have to be careful not to make a route that goes from Mars to Earth, back to Mars, then back to Earth when routed (for obvious reasons).
So for Earth-to-Mars payments, it's actually more efficient to use on chain transactions.
There's actually no concept of a single "Lightning Network". There are many LNs. Some networks use shitcoins, some use keysend or AMP, some use unannounced channels, some are a subset of what we call "mainnet" and some are not even payable from mainnet.
Martians could leverage this quality of LN to establish their own Lightning Network that exists entirely on Mars. They could use their mainnet to pay other martian nodes with ease. They would establish channels with each other by broadcasting a TX back to Earth. Then, they'd have to increase the time lock deltas on all their channels to give themselves more blocktime to respond to fraudulent force closes.