There is a difficulty in dealing with material written in another language: we often have a tendency to apply the rules of our own language to the other language. You are correct, I Corinthians 11:20 does not contain a singular article before the phrase Lord's Supper. The verse in Greek is: Sunerchomenôn oun humôn epi to auto ouk estin kuriakon deipnon phagein. The key words are:
estin: (it is) verb, third person singular, indicative, present tense, active voice
kuriakon: (Lord's) Accusative, singular, neuter
deipnon: (supper) noun, singular, neuter
Literally in English the phrase is "it is Lord's supper" but buried in the all the terms is that what is being discussed is singular. We express this in English by using a singular article, but in Greek such is not always necessary since the words contain case endings to indicate such ideas as singular versus plural, nominative versus accusative, and gender (masculine, feminine, or neuter). A part of the "joy" of learning Greek is the memorization of all the various case endings because they are critical in understanding the text. Yet it is these very case endings which give Greek its reputation for being a very precise language.
Therefore, the argument remains.
I have articles in my files both for and against multiple servings of the Lord's Supper on the first day of the week. If I can find the time this week, I'll try to find some of the better ones and add them to the website.