Then what in your opinion is the difference
between Lightning Network and Liquid Network?
Liquid Network is fundamentally different from the Lightning Network.
Liquid Network cannot work without third-party. You can exchange BTC to L-BTC on your own, but you won't be able to convert it back without Liquid Federation member's help. Liquid Network transactions are not instantaneous. Every minute, a new block is generated by one of the Functionaries and signed by the majority of other Functionaries. Functionaries are selected among the members of the Liquid Federation.
The Lightning Network on the other hand, does not suffer from many of the Liquid Network's problems. All you need to open and close a channel is a simple on-chain transaction. Funds are held in a 2-of-2 multisig address unlike Liquid Network where funds are stored in a 11-of-15 multisig address controlled by Liquid Network's Watchmen. The number of required confirmations before a channel becomes active is fully customizable while Liquid Network requires 102 confirmations before L-BTC is credited.
As for the Lightning transactions, HTLCs are used for trustless payment settlement. Every time a balance of the channel is updated, a new commitment transaction is signed to ensure that the current channel balance can be enforced on-chain. When that happens, sub-satoshi values are rounded down and outputs below the dust limit are added to the transaction fee. As of right now, subsatoshis are negligible values, which in my opinion can be discarded. It won't be a problem anymore if some day there is a hard-fork changing the maximum number of decimal places.
I think there are only two situations when
some trust is involved. The first one is when you have milisatoshis and you really care about them. As long as the channel is open, you can spend them. The other one is when your node goes offline for some reason which means that the other party can broadcast an old commitment transaction. You can freely set the amount of time which the other party must wait before the transaction can be included in a block after it was broadcast. Most nodes will accept timelocks up to 2046 blocks (~2 weeks), so it shouldn't be really a problem. I could mention watchtowers here, but they are obviously a third-party.
Having said all of that, I believe that the Lightning Network cannot be called a third-party off-chain system, especially if you compare it to Liquid Network.
Why is the Liquid network FAQ topic not included?
I don't recall ever seeing such a thread. That could be one of the reasons why it is not in this section. A separate board for second layer software would be probably the best solution.