God gave two ordinances to regulate and order local church membership: baptism and the Lord’s Supper. So inasmuch as the Lord’s Supper is a local church ordinance it should be administered by the pastoral leadership (with the assistance of the deacons or elders) in a local church setting (this is not to say it cannot be administered to shut-ins in their living quarters). For some churches a house may be their local church setting.
Since the Lord’s Supper is an ordinance (not a sacrament) designed to regulate and order a body of people, one side of its function is that it ties them together with simultaneous remembrance of the Lord’s death and communion with him. But the other side of its function is examination of your life before you enter His presence so that you can correct any irregularities in your self, and especially between you and any other member of the body. That is easy to imagine happening if the full body is assembled together for the service.
So just from a practical/scriptural standpoint, I don’t know if “cell groups” outside the local assembly really fulfill the function of the ordinance. Certainly a meal of fellowship can be had without calling it the Lord’s Supper. But it’s kind of like trying to fulfill the commission to make disciples outside the complete local church experience. Have you really made disciples if they are not established in the fellowship of a local body, scripturally defined, and anchored to its structure (including membership, giving, and the accountability of church discipline)?
How to Spot an Ordinance
1) There is sovereign institution and authorization
2) It symbolizes spiritual truth
3) There is a specific command for its perpetuation
4) There is Biblical evidence of historical fulfillment or practice
Four requirements should be fulfilled for someone to take part in the Lord’s supper:
A) Being regenerated
B) Being scripturally baptized
C) Being a current church member (someplace)
Requirements for membership wereD) Having an orderly walk
1) A credible testimony of regeneration, Acts 2:41
2) Baptism by officers of the local body, Acts 2:41
Some churches practice open communion. That means they do not check the credentials of anyone who participates. Some churches practice closed communion. That means they say you have to be a member of their particular local church to participate. We practice close communion. Any other baptized believer from a church of like faith and practice—who is living as he or she should—can participate.
There are multiple evidences of organization of local church membership in the New Testament. Organized membership
1) Met at stated times on the first day of the week, Acts 20:7; Heb 10:25
2) Had officers, Phil 1:1
3) Designated ministers, Acts 20:17,28
4) Recognized the authority of the local church and its pastors, Mat 18:17; 1 Pet 5:2; Heb 13:7,17
5) Exercised discipline of members, 1 Cor 5:4-5,13
6) Recorded contributions of members, Rom 15:26; 1 Cor 16:1-2
7) Granted letters of commendation when changing localities, Acts 18:27; 2 Cor 3:1
8) Had order, 1 Cor 14:40; Col 2:5