See the comments on verse 18, with which this verse is closely connected.

The Lord’s translates an adjective meaning “belonging to the Lord.” In Rev 1.10 it is used of Sunday as the Lord’s day.

The meaning of verse 20 must be partly understood in the light of the contrast with verse 21: “it is not the Lord’s Supper that you are eating; it is your own selfish individual meals.” Another possible translation is “even though you may think you are eating the Lord’s Supper, it is not so.”

Quoted with permission from Ellingworth, Paul and Hatton, Howard A. A Handbook on Paul’s First Letter to the Corinthians, 2nd edition. (UBS Handbook Series). New York: UBS, 1985/1994. For this and other handbooks for translators see here .