I see one verse that says "The Lord's Day" and it is only used once in Revelation. I did some research but cannot find any evidence that it points to a sabbath day or a day of rest.
Here is the verse,
"I was in the spirit on the Lord's Day and heard behind me a great voice as of a trumpet." Revelation 1:10
John was in the spirit and taken to a place in time where He saw all these things happening. I believe that he was taken to witness the Great and awesome coming of the Lord. Here is why I think that way:
"For it is the day of the Lord's vengeance, and the year of recompenses for the controversy of Zion" Isaiah 34:8
"And it shall come to pass in the day of the Lord's sacrifice, that I will punish the princes, and the king's children, and all such are clothed with strange apparel." Zephaniah 1:8
"Neither their silver nor their gold shall be able to deliver them in the day of the LORD'S wrath; but the whole land shall be devoured by the fire of his jealousy: for he shall make even a speedy riddance of all them that dwell in the land." Zephaniah 1:18
"Seek ye the LORD, all ye meek of the earth which have wrought his judgment; seek righteousness, seek meekness: it may be ye shall be hid in the day of the LORD'S anger." Zep 2:3
"But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up." 2 Peter 3:10
And these are all prophecy scriptures relating to the great and awesome arrival of our Lord. I believe that is the true Day of the Lord. The Day of the Lord is the day we all look forward to and anticipate. This is the day that He will claim His bride and recompense us.