I must admit that a reference to the Lord's supper in 1 Corinthians 5:1-13 is a possibility (cf. 1 Cor. 11:23ff). However, my analysis of this account rules out that conclusion for the following reasons.
1 Corinthians 5:1 describes the sin of a Christian brother in Corinth. He is cohabiting with his father's wife (living in an incestuous relationship); even worse, the older men of Corinth--representing the EKKLESIA--are tolerating this immoral conduct. Paul laments that the Corinthians are "puffed up" rather than mourning over the abhorrent deeds of the immoral brother in their midst.
In 1 Cor. 5:3-5, the "apostle to the nations" recommends that the one practicing sin be "delivered up to the adversary." This act is done in order to destroy the sinful "flesh" and preserve the spirit of the believer "in the day of the Lord."
Next, Paul continues to expound on the reason that the sinning believer must be turned over to the Devil. By allowing this one to remain in the midst of the congregation, the EKKLESIA will suffer corruption: it will not be able to rightly observe the antitypical passover: "for even our Paschal Lamb, Christ, was sacrificed" (Emphatic Diaglott). Therefore, the congregation of God must take the action prescribed in 1 Cor. 5:9-13. What is the thrust of this counsel? What action is the EKKLESIA urged to take?
1 Cor. 5:11 says: "NUNI DE EGRAYA hUMIN MH SUNANAMIGNUSQAI EAN TIS ADELFOS ONOMAZOMENOS hH PORNOS . . ."
The phrase that really catches my attention here is NUNI DE EGRAYA hUMIN
This part of the verse indicates that Paul is not simply talking about ceasing to share "the meal" with a brother who practices sin--although clearly the EKKLHIA should take this action as well.
The present infinitive middle SUNANAMIGNUSQAI tells me that all association should cease with this person (not just the Lord's evening meal). Elsewhere we are told, "do not receive him into your house nor wish him success" (2 John 10, 11). If you want to discuss the applicability/inapplicability of 2 John 2:7, we can examine that verse too. In sum, I would say that 1 Cor. 5:11 is talking about general association (i.e., "don't even eat lunch with this man"!).
Kathleen Callow makes this point concerning 1 Cor. 5:6-8:
"In this unit Paul urges the expulsion (EKKAQARATE, v. 7a) in the light of the effect of evil on their fellowship as a whole, and of their own status as AZOUMOI--a purified community" (See Linguistics and NT Interpretation, edited by D.A. Black, page 202).
Robertson's Word Pictures supplies this note on 1 Cor. 5:11:
"With such a one, no, not to eat (τωι τοιουτωι μηδε συνεστιειν — tōi toioutōi mēde sunesthiein). Associative instrumental case of τοιουτωι — toioutōi after συνεστιειν — sunesthiein 'not even to eat with such a one.' Social contacts with such 'a brother' are forbidden."