I haven't read the paper in full yet so grain of salt but I suspect the benefit to lightning would be that coins/utxos in a pool could be used to create lightning channels making lightning a 3rd layer with a coin pool serving as a 2nd layer. Basically, you wouldn't require a on-chain coins/utxos to make a lightning channel which is awesome because we all assume on-chain txs will likely be very expensive in the future.