Lightning network at Ethereum or Bitcoin are pretty similar to the concept of private chains at Hyperledger Fabric. They simply define am off-chain channel that is hooked at the beginning and at the end to the Blockchain, but otherwise the transactions are running independently from the Blockchain, On the contrary, private transactions at Quorum can be regarded as the other side of the coin: as the transactions are running on the Blockchain, they are encrypted and only certain nodes with the necessary key are able to decrypt. The state transition of the private transactions are saved however into a special state, called private state that is separated from the private state. In this sense private channels make a splitting or sharding on the Blockchain itself as private transactions make a splitting or sharding in the state. Certainly the top is the proposed classical Ethereum sharding, in which both the state and the transaction chain are spitted into pieces.
Figure 1, different types of sharding