No, they cannot "compress" the current data, but with the adoption of the segwit they can process more transactions using the same amount of data
Including more transaction into one block still doesn't reduce the size of the blockchain.
Regardless of segwit/non-segwit blocks are (mostly) full.
and the lightning network can reduce the use of registry in blockchain since we can make all outside the network.
Blocks still will be mined at the same rate.
And if the mempool would be empty (because somehow everyone is using LN without closing channels, whatsoever..) transactions with 1 sat/B would be confirmed within 1 block,
leading to people using on-chain transactions to pay merchants etc.. again.
Why should someone fund a channel and use the LN if fees would be 1 sat/B ? -> This will lead to full blocks again.
So, no. The lightning network does not decrease the size of the blockchain.