As far as I can understand it from the feature description, it has nothing to do with the lightning network.
The only effect from the mentioned operation is a bump (increment) of the account sequence number, which can be useful for complex use cases.
A typical use for this is to allow invalidating large ranges of transactions that were pre-shared with others when implementing complex multi-party transactions that form workflows.
The difference is that in the event that a transaction is invalidated by an operation from a different transaction, it would fail (collecting fees).
So if you are using the
BumpSequenceOp it means that you decline all other concurrent transactions on the account. They will fail because
BumpSequenceOp alters the account sequence.
The bump itself can be useful for the "smart contract" cases, for example, escrow operations.