The importance of Sunday as the Lord's Day in Catholicism has to do with the day of Jesus' resurrection.  He died on a Friday, laid in the tomb on a Saturday, and rose again on a Sunday.

Thus, Jesus fulfills the Mosaic Law, resting from His work on the Sabbath.  His resurrection is the beginning of a new creation.

Thus, Catholics worship the Lord on the first day of the new creation, rather than resting on the last day of the old.