I guess, from both your answers, it is useful to divide on lightning network if required but not outside it 

allark

Yes, but millisats are what makes a single sat spendable 

Sats are the only units in the mainnet. Bitcoin itself as a unit doesn't exist. Every transaction is in sats.

You can't take a single sat on chain either. Any UTXO amount below the dust limit is essentially unspendable due to the fees required to spend it. Millisats exist in a similar way that sats exist. As an accounting unit. Not necessarily a discrete and fully transferable unit. 

nullcount

bitcoin

Is a Satoshi infinitely divisible?

Dividing satoshis is risky as on the mainnet there are only statoshi. So you cannot take back your milli sats to the mainnet. 