Makes it easier to scale on-chain with more transactions as signaling between nodes becomes easier at higher block sizes, but that is for the future when blocks starts to get filled.
If my understanding is correct it means that Graphene makes it possible for miners to signal that a block was found by sending a small fingerprint to other nodes.
Let's say Graphene is implemented. We are already paying 1 sat per byte, so this means it won't even reduce our fees. Also BTC's Lightning apparently has an mSat amount (0.001 sats)