Thank BBerean for noticing the Matt 24:20 scripture about the sabbath and the Revelation 1 verse about how John was in the spirit on the Lord's Day.
The Lord's Day in Revelation 1 is probably referring to the Day of the Lord, such as is talked about in Malachi 4. This is a time when the proud are burned up and those who fear his name arise with healing in his wings. Note that John turned and looked behind him to get the messages for the church, and this was from his position of the Lord's Day, so he's looking back into the church age if you will. Possibly, then, this Lord's Day is a time at the end of the church age. This is also likely to be the time referred to as the Sabbath in Matt 24. The flight mentioned is necessary before the Lord's Day, the Day of the Lord, before the Sabbath, because the flight mentioned is addressing how true believers come out of the fallen congregations or ideologies before the judgment takes effect. The judgment takes effect on the Sabbath, which is said to be the time of great tribulation. As with any sabbath, this end time period is not talking about a ritual of going to a building on a certain day, but about being saved versus being unsaved.