"Lord's day" is a fine translation for KURIAKHN. While it is true that KURIAKOS evidently has the meaning, "that which pertains or belongs to the Lord" in 1 Cor. 11:20, it most surely is used for the "Lord's day" when John writes:
EGENOMHN EN PNEUMATI EN THi KURIAKH hMERA (Rev. 1:10).
Of course, John makes it explicit that he is referring
to the Lord's day, whereas Ignatius of Antioch simply employs
KURIAKHN, though the context and conventional usage of
KURIAKOS may point to the Greek term in this case having
reference to the Lord's day; but this does not
necessarily mean that we should construe the "Lord's
day" in Revelation as Sunday.
On the other hand, Louw-Nida states that KURIAKOS
denotes: "pertaining to the Lord" or "belonging to the
Lord, Lord's" (See semantic domain 12.10).
BDAG (under KURIAKOS) also has an interesting note
about Magnesians 9.1:
"KATA KURIAKHN ZHN observe the Lord's day (opp.
SABBATIZEIN) IMg 9:1 (on the omission of hHMERA cp.
Jer. 52:12 DEKATHi TOU MHNOS and s. AGORAIOS 2)."
I believe the note in BDAG may be helpful on this
point. M. Holmes also translates the rest of Magnesians 9:1:
"on which our life also arose through him and his
death (which some deny) . . ."
In closing, I equally found an informative note about
KURIAKOS in David Aune's commentary on Revelation 1-5
(pp. 83-84) including the papyrological employment of
the word. Aune argues that Ignatius has Sunday in mind
at Magnesians 9:1. That may be correct, even though I
don't believe John refers to Sunday in Rev. 1:10.