So what happens when Lightening Network gets flooded with endless exchanger transactions and acceptance from more and more exchangers in the future?
Such thing won't happen from night to day. I would say it will follow the market rules. The more need for open and closing channels, the more channels will be created, more liquidity, more development, more features, more security, more everything.
We have only a handfull(

) LN implementations. Probably, if demand "demands" more implementations will appear and more offer there will be.
I am curious about the concept of LN. Will it be same story with LN in the future if exchangers start adopting it for the escape from current bitcoin network congestion? Definitely LN is on chain and will get many restrictions as it grows. In similar fashion as bitcoin network did.
I have no idea how one could elaborate a rationale on that as it may depend on so many factors that is quite hard to predict a possible path. Once more, I would say that will also follow what the market demands, even in conceptual terms. When there is a problem / challenge, I'm pretty sure that there are enough bright people to think out pretty advanced solutions to satisfy the demand.
The current issue is with Ordinal NFT which can be upgraded "on chain" meaning they are putting extra burden on the chain with numerous packets moving in and out.
Wouldn't that be the same case with LN in the future. Also, will this ever stop like this or we need to keep forming new type of networks one after another. Please ignore my less technical background in the field of blockchain and how it works, I am still prospering on that side.
Not exactly sure what you mean "to be the same case with LN". LN needs the L1 and it is supposed to need as it's the base layer that provides the critical features to all layers above, such as decentralization, security and all other properties. And LN is actually helping the base layer to handle the bourdain of handling the increasing number of transaction and also handling the speed that we can make transactions, theoretically competing with other fiat systems such as VISA.