My question is: Is it possible to stop the block generation when mempool is empty?
Impossible, miner will just mine empty block (block which only contain coinbase transaction). Here are few example (each from different pool),
https://blockchair.com/bitcoin/block/677543
https://blockchair.com/bitcoin/block/677425
https://blockchair.com/bitcoin/block/677026
https://blockchair.com/bitcoin/block/676838
https://blockchair.com/bitcoin/block/676811
OK! So this Lightning Bitcoin isn't THE Lightning Network ? 
https://coinmarketcap.com/currencies/lightning-bitcoin/
Now I think it's better to use Lightning than a custom layer 2.
https://coinmarketcap.com/currencies/lightning-bitcoin/
Now I think it's better to use Lightning than a custom layer 2.
No, their GitHub page (github[dot]com/lbtcio) even say so
Quote
Lightning Bitcoin is a fork of the Bitcoin blockchain at the block 499,999, with DPoS consensus mechanism and 2M block size.