What is a Lay Communion Service?
It is a Sunday Celebration in the Absence of a Priest (SCAP)
20. Among the forms of celebration found in liturgical tradition when Mass is not possible, a celebration of the word of God is particularly recommended,  and also its completion, when possible, by eucharistic communion. In this way the faithful can be nourished by both the word of God and the body of Christ. "By hearing the word of God the faithful learn that the marvels it proclaims reach their climax in the paschal mystery, of which the Mass is a sacramental memorial and in which they share by communion."  Further, in certain circumstances the Sunday celebration can be combined with the celebration of one or more of the sacraments and especially of the sacramentals and in ways that are suited to the needs of each community.
21. It is imperative that the faithful be taught to see the substitutional character of these celebrations, which should not be regarded as the optimal solution to new difficulties nor as a surrender to mere convenience.  Therefore a gathering or assembly of this kind can never be held on a Sunday in places where Mass has already been celebrated or is to be celebrated or was celebrated on the preceding Saturday evening, even if the Mass is celebrated in a different language. Nor is it right to have more than one assembly of this kind on any given Sunday.
28. When Mass cannot be celebrated, the pastor is to ensure that holy communion be given. He is also to see to it that there is a celebration of the eucharist in due time in each community. The consecrated hosts are to be renewed often and kept in a safe place.
29. As the primary assistants of priests, deacons are called in a special way to lead these Sunday assemblies. Since the deacon has been ordained for the nurture and increase of the people of God, it belongs to him to lead the prayers, to proclaim the gospel, to preach the homily, and to give communion. 
30. In the absence of both a priest and a deacon, the pastor is to appoint laypersons, who are to be entrusted with the care of these celebrations, namely, with leading the prayers, with the ministry of the word, and with giving holy communion
Those to be chosen first by the pastor are readers and acolytes who have been duly instituted for the service of the altar and of the word of God. If there are no such instituted ministers available, other laypersons, both men and women, may be appointed; they can carry out this responsibility in virtue of their baptism and confirmation.  Such persons are to be chosen in view of the consistency of their way of life with the Gospel and in the expectation of their being acceptable to the community of the faithful. Appointment is usually to be for a definite time and is to be made known publicly to the community. It is fitting that there be a celebration in which prayers are offered to God on behalf of those appointed. 
The pastor is to see to the suitable and continuous instruction of these laypersons and to prepare with them worthy celebrations (see Chapter III).
31. The laypersons appointed should regard the office entrusted to them not so much as an honor but as a responsibility and above all as a service to their brothers and sisters under the authority of the pastor. For theirs is not a proper office but a suppletory office, since they exercise it "where the need of the Church suggests in the absence of ministers." 
Those who are appointed to such an office "should do all of, but only, those parts which pertain to that office."  They should carry out their office with sincere devotion and the decorum demanded by such a responsibility and rightly expected of them by God's people. 
32. When on a Sunday a celebration of the word of God along with the giving of holy communion is not possible, the faithful are strongly urged to devote themselves to prayer "for a suitable time either individually or with the family or, iff possible, with a group of families."  In these circumstances the telecast of liturgical services can provide useful assistance.
33. Particularly to be kept in mind is the possibility of celebrating some part of the liturgy of the hours, for example, morning prayer or evening prayer, during which the Sunday readings of the current year can be inserted. For "when the people are invited to the liturgy of the hours and come together in unity of heart and voice, they show forth the Church in its celebration of the mystery of Christ."  At the end of such a celebration communion may be given (see no. 46).
34. "The grace of the Redeemer is not lacking for individual members of the faithful or entire communities that, because of persecution or a lack of priests, are deprived of celebration of the eucharist for a short time or even for a long period. They can be moved by a deep desire for the sacrament and be united in prayer with the whole Church. Then when they call upon the Lord and raise their minds and hearts to him, through the power of the Holy Spirit they enter into communion with Christ and with the Church, his living body . . . and therefore they receive the fruits of the eucharist."