Where does it say that? Not once in scripture does it call the first day of the week "the Lord's day".
Consider the commonly observed day, the day of His resurrection and heavenly sacrifice of His Blood, in which the followers of Jesus engage in the Remembrance, to honor Him as Lamb of God and Lord of Creation, and to rejoice in the reconciliation with His Father.
Act 20:7 And upon the first day of the week, when the disciples came together to break bread, Paul preached unto them, ready to depart on the morrow; and continued his speech until midnight.
1 Co_16:2 Upon the first day of the week let every one of you lay by him in store, as God hath prospered him, that there be no gatherings when I come.
The first day of the week also reminds us of the day the Holy Spirit was poured out, on and into His People, as prophesied for the Pentecost:
Lev. 23:16 Even unto the morrow after the seventh sabbath shall ye number fifty days; and ye shall offer a new meat offering unto the LORD.
It was on this first day of the week that John received the Word of the Apocalypse from The Christ:
Rev. 1:10 I was in the Spirit on the Lord's day, and heard behind me a great voice, as of a trumpet, . . .