he Lightning Network: with third-party and scriptSig malleability fixed, the Lightning Network is less complicated to implement and significantly more efficient in its use of space on the blockchain. With scriptSig malleability removed, it also becomes possible to run lightweight Lightning clients that outsource monitoring the blockchain, instead of each Lightning client needing to also be a full Bitcoin node.
I don't think that it is necessary for lightning to be a full node. It can still work without being a full node but with some additional complexity. Where in the lightning paper does it say that a full node is required?
That little tidbit of info comes from Bitcore
https://bitcoincore.org/en/2016/01/26/segwit-benefits/The Lightning Network: with third-party and scriptSig malleability fixed, the Lightning Network is less complicated to implement and significantly more efficient in its use of space on the blockchain. With scriptSig malleability removed, it also becomes possible to run lightweight Lightning clients that outsource monitoring the blockchain,
instead of each Lightning client needing to also be a full Bitcoin node.
Do you not understand the Word OFFCHAIN , BTC is only Locked on the ONLINE BLOCKCHAIN, it is not and can not be moved onto LN's network,
So you are trading BTC IOUs when you use LN.
The Lightning Network conducts transactions by creating Bitcoin transactions that can be broadcast onto the Bitcoin network at any time. There are no IOUs being traded, what is happening is that transactions are being created but not broadcast. Again, there is no separate thing where Bitcoin is being converted into some sort of IOU on lightning.
LN is OFFCHAIN, unless it is ONCHAIN, it is LITERALLY IMPOSSIBLE for BTC to be on it , meaning you have BTC IOUs on LN.
In other words , since BTC can not exist Offchain, What LN lists as a BTC is merely a debt for BTC, which is paid upon completion of contracts.
IOU => is usually an informal document acknowledging debt (In Theory : Using advanced features LN may even allow only certain miners to process the transaction Fees when Onchain BTC Transactions are required.)
(Giving LN Nodes the ability to starve miners not in Collusion with them of transaction fees. ) 
Now that is just FUD. How would LN only allow certain miners to confirm those transactions? That is just completely false.
One of the Concerns in the LN Network Whitepaper is that ,
Miners may Decline Certain LN transactions so their Locks timeout and the BTC can be Stolen.
If the above is possible, the reverse is also possible which makes what I said a Valid Theory.
That risk is based on miner collusion. The reverse would also require miner collusion, not some technical aspect of LN that makes it possible for only specific miners to mine those transactions. This is not just something related to LN but rather an issue that can already happen with Bitcoin as it is because it is just miner collusion and requiring human intervention in order for that to be possible.
not some technical aspect of LN that makes it possible for only specific miners to mine those transactions.
Until LN has been up and running for a year or so , You don't really know what additional feature could be installed.
They are including an option so the miner can induce an option to ignore a block, so it does not affect the time lock, under certain attack conditions.
Adding a rotating passcode so LN knows to only include it's transactions in a Block from a specific miner , is also not out of the realm of possibility.
Would they do it , hopefully not, but would it be possible, yes it would, which is why I said Theory and not fact.