Since there is no commission for miners for transactions in this network.
I don't think anyone would pay a few thousand sats for a 1 sat transaction. While miners don't earn money on the Lighting Network transactions, they are paid for establishing and settling down the balance of Lightning Network channels.
Is it possible that the Lightning network in the future will adversely affect the security of the Bitcoin network?
The Lightning Network can't function without the blockchain. It won't replace on-chain transactions. It might decrease some of the load and encourage people to spend Bitcoin on small things since it won't cost a fortune.