Complex sentence: Currently the main use of hash lists is to make sure that data blocks received from other peers in a peer-to-peer network are received undamaged and unaltered, and to check that the other peers do not "lie" and send fake blocks.
Split into simpler sentences: Currently the main use of hash lists is to make sure that data blocks received from other peers in a peer-to-peer network are received undamaged and unaltered. And even to check that the other peers do not lie and send fake blocks.