The core lightning security assumption relies on a punishment mechanism called “Justice Transaction”. However, how can you prevent a malicious user from colluding with a miner, and producing a block with old state transactions without the rest of the network (watchtowers/honest nodes) realising it pre-mining?
When a channel is closed unilaterally, it requires two transactions by the closing party to move funds from a channel back into unilateral control.
The closing party publishes their version of the commitment transaction to the network. The commitment transaction has a special condition for the closer's output. After the commitment transaction is included in a block, the closing party's funds are locked for a period of time in which only the counterparty is able to issue their penalty transaction. The closing party can only spend their output after the lock expires. Since the two spending conditions are encoded in the output's locking script, the funds remain subject to potential penalty spending until the closing party moves the funds to a different output.
To prevent a penalty transaction from occurring during the wait period, the attacker would need to be able to censor the penalty transaction from being included in any block between the commitment transaction being confirmed and the lock expiring. Censorship of such level would require sufficient hashrate to reorganize any block that includes it.
It's named "penalty transaction" by the specs :).
Regarding your core question, you are right but this also requires this miner to be able to heal this block chain without a censored (the penalty) transaction. It therefore assumes that a single miner has more hashpower than the rest of the network combined.
Thus it can be stated as such:
The Lightning Network core security assumption relies on the fact that nobody can "51% attack" the network.
The decentralization of mining is a huge deal for Lightning (and all other L2s i know of).
This is a special case of 51% attack.
The lock of the funds in a force-close is at a minimum 144 blocks for the person who submit the old state, but the other party can claim their share at once. They can also submit a penalty transaction at once, and have all the funds in a channel to spend from.
So 144 is how many blocks that had to be mined in secret to pull this off.
And yes, it would have to be a majority, because the chain with the most PoW wins.
In theory it is possible, but it's impossible in the same way that 6 blocks is seen as immutable - it is not likely to yield gains worth the expenditure, to pull it off.
If they had that hash rate and the willigness to steal, they'd be more likely doublespend a transaction to an exchange, because that is easier.
You can't as described here:
Tl,dr: if one controlls more than 50% of hashrate and secretly mines the longest chain with old state one can steal the entire capacity of all channels one is connected to. Reward is much higher than regular Bitcoin double spent through reorg but execution is also more expensive