Lightning network in real world
With lightning network, my understanding is that we would be making a transaction on a &quot;side chain&quot;

The lightning network is not a ‘side chain’, that term is usually used to describe an entirely different piece of technology that can be built to work on top of/alongside bitcoin.

Does the lightning network also solve the problem of giving confidence to the cashier that I have the money required?

Yes, lightning payments can settle pretty much instantly, both the customer and cashier would see proof of this in their respective lightning wallet applications. There is no need to wait for an on-chain transaction to be confirmed.