Segwit makes it easier to track your Transactions.
In what way? The way that inputs and outputs work are still exactly the same.
SegWit : Makes it So a LN Node does not have to run a full Bitcoin node
How so? An LN Node doesn't need to be a full Bitcoin node already. They can work fine as SPV wallets now and after Segwit. Segwit does not change that at all.
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.
What requires a Lightning client to be a full node? As I understand it, it doesn't matter, and segwit does not change that.
Simply put SegWit will make it possible to Steal BTC Value to use in LN Alternative Payment System using BTC IOUs .
I don't think you understand how LN works. LN does not issue IOUs. It creates very real, valid, and broadcastable Bitcoin transactions. There are no IOUs involved.
Miners will lose money because LN can decrease the number of OnChain Transactions.
Not necessarily. LN is not for every type of transaction. It is really only good for small, repeated transactions like faucet payments.
(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.
The only thing LN does is limit fees for miners and give those fees to owners of Lightning Network (Blockstream)
Blockstream does not own the Lightning Network. LN is an open source spec that is being implemented by multiple teams, it has not owner nor controller.
Regardless, discussing LN in this thread is off topic.
You are demonstrating and extreme lack of knowledge on subjects you are arguing against. I highly suggest that you actually do some research before posting.
Please stop spreading FUD.