Who is responsible for the integrity of intermediate transactions that are going on once channel is open and before its closed?
~~~
There are additional complex systems built on top of that in order to encourage honesty and punish any attempted theft. For example, if the latest transaction we had signed was 1.6 BTC to me and 0.4 BTC to you, but you tried to broadcast an old transaction which splits the funds 1 BTC each, there is a mechanism to allow me to dispute that and claim all the funds for myself, meaning you lose everything as punishment for the attempted theft.
If we combine your last two replies here about Lightning Network then they are very short and informative explanation about Lightning network.
LN solves Bitcoin scalability issues but the reason why LN failed to take off (which I infer from your last explanation) is since most of the transactions are managed by LN not by the bitcoin network. Bitcoin network has developed its trust over a period of time and there is no other network that is widely trusted by so many people globally.
If solving scalability issue alone can take you to moon then there are thousands of tokens that are super fast when compared to Bitcoin.